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Machine learning potentials, particularly the deep potential (DP) model, have revolutionized molecular dynamics (MD) simulations, striking a balance between accuracy and computational efficiency. To facilitate the DP model's integration with the popular MD engine OpenMM, we have developed a versatile OpenMM plugin. This plugin supports a range of applications, from conventional MD simulations to alchemical free energy calculations and hybrid DP/MM simulations. Our extensive validation tests encompassed energy conservation in microcanonical ensemble simulations, fidelity in canonical ensemble generation, and the evaluation of the structural, transport, and thermodynamic properties of bulk water. The introduction of this plugin is expected to significantly expand the application scope of DP models within the MD simulation community, representing a major advancement in the field. [ABSTRACT FROM AUTHOR]

Cluster molecular magnets prove their potential for applications in quantum technologies, encouraging studies of quantum entanglement in spin systems. In the paper we discuss quantum entanglement properties of pentamer cluster composed of spins S = 1 / 2 forming a tetrahedron with additional spin in its center, with geometry reproducing the smallest nonplanar graph. We model the system with isotropic Heisenberg Hamiltonian including external magnetic field and use exact diagonalization approach to explore the ground-state phase diagram and thermodynamic properties within canonical ensemble formalism. We focus the interest on two-spin entanglement quantified by Wootters concurrence. For ground state, we find two states with total cluster spin equal to 3/2 exhibiting entanglement, occurring preferably for antiferromagnetic interactions. For finite temperatures, we predict the presence of magnetic-field-induced entanglement as well as temperature-induced entanglement. [ABSTRACT FROM AUTHOR]

We discuss novel many-fermions thermodynamics' features. They refer to the energy cost associated to order-disorder changes. Our thermal quantum statistical scenario is controlled by suitable fermion-fermion interactions. We deal with two well-known quantum interactions that operate within an exactly solvable model. This model is able to adequately describe some aspects of fermion-dynamics, particularly level-crossings. We describe things via employment of Gibbs' canonical ensemble strictures. We show that judicious manipulation of the energy cost associated to statistical order (disorder) variations generates useful information-quantifiers. The underlying idea is that changes in the degree of order are intimately linked to level-crossings energetic costs. [ABSTRACT FROM AUTHOR]

The dynamic and thermodynamic properties of nanoclusters are studied in two different environments: the canonical and microcanonical ensembles. A comparison is made to thermodynamic properties of the bulk. It is shown that consistent and reproducible results on nanoclusters can only be obtained in the canonical ensemble. Nanoclusters in the microcanonical ensemble are trapped systems, and inconsistencies will be found if thermodynamic formalism is applied. An analytical model is given for the energy dependence of the phase space volume of nanoclusters, which allows the prediction of both dynamical and thermodynamical properties. [ABSTRACT FROM AUTHOR]

Here, we investigate how the local properties of particles in a thermal bath may influence the thermodynamics of the bath, and consequently alter the statistical mechanics of subsystems that comprise the bath. We are guided by the theory of small-system thermodynamics, which is based on two primary postulates: that small systems can be treated self-consistently by coupling them to an ensemble of similarly small systems, and that a large ensemble of small systems forms its own thermodynamic bath. We adapt this "nanothermodynamics" to investigate how a large system may subdivide into an ensemble of smaller subsystems, causing internal heterogeneity across multiple size scales. For the semi-classical ideal gas, maximum entropy favors subdividing a large system of "atoms" into an ensemble of "regions" of variable size. The mechanism of region formation could come from quantum exchange symmetry that makes atoms in each region indistinguishable, while decoherence between regions allows atoms in separate regions to be distinguishable by their distinct locations. Combining regions reduces the total entropy, as expected when distinguishable particles become indistinguishable, and as required by a theorem in quantum mechanics for sub-additive entropy. Combining large volumes of small regions gives the usual entropy of mixing for a semi-classical ideal gas, resolving Gibbs paradox without invoking quantum symmetry for particles that may be meters apart. Other models presented here are based on Ising-like spins, which are solved analytically in one dimension. Focusing on the bonds between the spins, we find similarity in the equilibrium properties of a two-state model in the nanocanonical ensemble and a three-state model in the canonical ensemble. Thus, emergent phenomena may alter the thermal behavior of microscopic models, and the correct ensemble is necessary for fully-accurate predictions. Another result using Ising-like spins involves simulations that include a nonlinear correction to Boltzmann's factor, which mimics the statistics of indistinguishable states by imitating the dynamics of spin exchange on intermediate lengths. These simulations exhibit 1/f-like noise at low frequencies (f), and white noise at higher f, similar to the equilibrium thermal fluctuations found in many materials. [ABSTRACT FROM AUTHOR]

The ideal gas model is an important and useful model in classical thermodynamics. This remains so for small systems. Molecules in a gas can be adsorbed on the surface of a sphere. Both the free gas molecules and the adsorbed molecules may be modeled as ideal for low densities. The adsorption energy, U s , plays an important role in the analysis. For small adsorbents this energy depends on the curvature of the adsorbent. We model the adsorbent as a sphere with surface area Ω = 4 π R 2 , where R is the radius of the sphere. We calculate the partition function for a grand canonical ensemble of two-dimensional adsorbed phases. When connected with the nanothermodynamic framework this gives us the relevant thermodynamic variables for the adsorbed phase controlled by the temperature T, surface area Ω , and chemical potential μ. The dependence of intensive variables on size may then be systematically investigated starting from the simplest model, namely the ideal adsorbed phase. This dependence is a characteristic feature of small systems which is naturally expressed by the subdivision potential of nanothermodynamics. For surface problems, the nanothermodynamic approach is different, but equivalent to Gibbs' surface thermodynamics. It is however a general approach to the thermodynamics of small systems, and may therefore be applied to systems that do not have well defined surfaces. It is therefore desirable and useful to improve our basic understanding of nanothermodynamics. [ABSTRACT FROM AUTHOR]

The thermodynamic properties of the interacting particle–antiparticle boson system at high temperatures and densities were investigated within the framework of scalar and thermodynamic mean-field models. We assume isospin (charge) density conservation in the system. The equations of state and thermodynamic functions are determined after solving the self-consistent equations. We study the relationship between attractive and repulsive forces in the system and the influence of these interactions on the thermodynamic properties of the bosonic system, especially on the development of the Bose–Einstein condensate. It is shown that under "weak" attraction, the boson system has a phase transition of the second order, which occurs every time the dependence of the particle density crosses the critical curve or even touches it. It was found that with a "strong" attractive interaction, the system forms a Bose condensate during a phase transition of the first order, and, despite the finite value of the isospin density, these condensate states are characterized by a zero chemical potential. That is, such condensate states cannot be described by the grand canonical ensemble since the chemical potential is involved in the conditions of condensate formation, so it cannot be a free variable when the system is in the condensate phase. [ABSTRACT FROM AUTHOR]

The aim of the present paper is to provide a preliminary investigation of the thermodynamics of particles obeying monotone statistics. To render the potential physical applications realistic, we propose a modified scheme called block-monotone, based on a partial order arising from the natural one on the spectrum of a positive Hamiltonian with compact resolvent. The block-monotone scheme is never comparable with the weak monotone one and is reduced to the usual monotone scheme whenever all the eigenvalues of the involved Hamiltonian are non-degenerate. Through a detailed analysis of a model based on the quantum harmonic oscillator, we can see that: (a) the computation of the grand-partition function does not require the Gibbs correction factor n ! (connected with the indistinguishability of particles) in the various terms of its expansion with respect to the activity; and (b) the decimation of terms contributing to the grand-partition function leads to a kind of "exclusion principle" analogous to the Pauli exclusion principle enjoined by Fermi particles, which is more relevant in the high-density regime and becomes negligible in the low-density regime, as expected. [ABSTRACT FROM AUTHOR]

We study the thermodynamic limit of very long walks on finite, connected, non-random graphs subject to possible random modifications and transportation capacity noise. As walks might represent the chains of interactions between system units, statistical mechanics of very long walks may be used to quantify the structural properties important for the dynamics of processes defined in networks. Networks open to random structural modifications are characterized by a Fermi–Dirac distribution of node's fugacity in the framework of grand canonical ensemble of walks. The same distribution appears as the unique stationary solution of a discrete Fokker–Planck equation describing the time evolution of probability distribution of stochastic processes in networks. Nodes of inferior centrality are the most likely candidates for the future structural changes in the network. [ABSTRACT FROM AUTHOR]

Since the grand partition function Z q for the so-called q-particles (i.e., quons), q ∈ (− 1 , 1) , cannot be computed by using the standard 2nd quantisation technique involving the full Fock space construction for q = 0 , and its q-deformations for the remaining cases, we determine such grand partition functions in order to obtain the natural generalisation of the Plank distribution to q ∈ [ − 1 , 1 ] . We also note the (non) surprising fact that the right grand partition function concerning the Boltzmann case (i.e., q = 0 ) can be easily obtained by using the full Fock space 2nd quantisation, by considering the appropriate correction by the Gibbs factor 1 / n ! in the n term of the power series expansion with respect to the fugacity z. As an application, we briefly discuss the equations of the state for a gas of free quons or the condensation phenomenon into the ground state, also occurring for the Bose-like quons q ∈ (0 , 1) . [ABSTRACT FROM AUTHOR]

In this paper, I present Diatomic, an open-source Excel application that calculates molar thermodynamic properties for diatomic ideal gases. This application is very easy to use and requires only a limited number of molecular constants, which are freely available online. Despite its simplicity, Diatomic provides methodologies and results that are usually unavailable in general quantum chemistry packages. This application uses the general formalism of statistical mechanics, enabling two models to describe the rotational structure and two models to describe the vibrational structure. In this work, Diatomic was used to calculate standard molar thermodynamic properties for a set of fifteen diatomic ideal gases. A special emphasis was placed on the analysis of four properties (standard molar enthalpy of formation, molar heat capacity at constant pressure, average molar thermal enthalpy, and standard molar entropy), which were compared with experimental values. A molecular interpretation for the molar heat capacity at constant pressure, as an interesting pedagogical application of Diatomic, was also explored in this paper. [ABSTRACT FROM AUTHOR]

This review provides a critical assessment of the current state of affairs regarding the solvation thermodynamics involving mixed-solvent systems. It focuses specifically on (i) its rigorous molecular-based foundations, (ii) the underlying connections between the microstructural behavior of the mixed-solvent environment and its thermodynamic responses, (iii) the microstructural characterization of the behavior of the mixed-solvent environment around the dilute solute via unique fundamental structure-making/-breaking functions and the universal preferential solvation function, (iv) the discussion of potential drawbacks associated with the molecular simulation-based determination of thermodynamic preferential interaction parameters, and (v) the forensic examination of frequent modeling pitfalls behind the interpretation of preferential solvation from experimental data of Gibbs free energy of solute transfer. [ABSTRACT FROM AUTHOR]

We review constructions of three-dimensional 'quantum' black holes. Such spacetimes arise via holographic braneworlds and are exact solutions to an induced higher-derivative theory of gravity consistently coupled to a large-c quantum field theory with an ultraviolet cutoff, accounting for all orders of semi-classical backreaction. Notably, such quantum-corrected black holes are much larger than the Planck length. We describe the geometry and horizon thermodynamics of a host of asymptotically (anti-) de Sitter and flat quantum black holes. A summary of higher-dimensional extensions is given. We survey multiple applications of quantum black holes and braneworld holography. [ABSTRACT FROM AUTHOR]

Classical (MD) and ab initio (AIMD) molecular dynamics simulations were conducted to investigate the fundamental properties of solid and liquid MgO. AIMD was performed by DFT using the Strongly Conditioned and Appropriately Normed (SCAN) exchange correlation functional. The obtained pair-correlation functions of liquid MgO were used as reference data for the optimization of parameters of classical MD. For the latter, a Born–Mayer–Huggins (BMH) potential was applied, and parameters were adjusted until a best fit of both structural properties was obtained by AIMD and physical properties by experimental data. Different structural, dynamic and thermodynamic properties of solid and liquid MgO were then calculated by classical MD and compared with the literature data. Good agreement was found for the Mg-O bond length, self-diffusion coefficients, density of liquid MgO and for heat content and density of crystalline MgO. Using a void-melting approach, the melting temperature of MgO was found as 3295 ± 30 K, which is in good agreement with the recent experimental work by Ronchi et al. (3250 ± 20 K). The optimized parameters of BMH potential describe well the structural, dynamic and thermodynamic properties of solid and liquid MgO and may be combined with our previous results of a CaO-Al2O3-TiO2 system to calculate the properties of a quaternary CaO-MgO-Al2O3-TiO2 system. [ABSTRACT FROM AUTHOR]

Equilibrium density fluctuations at the molecular level produce cavities in a liquid and can be analyzed to shed light on the statistics of the number of molecules occupying observation volumes of increasing radius. An information theory approach led to the conclusion that these probabilities should follow a Gaussian distribution. Computer simulations confirmed this prediction across various liquid models if the size of the observation volume is not large. The reversible work required to create a cavity and the chance of finding no molecules in a fixed observation volume are directly correlated. The Gaussian formula for the latter probability is scrutinized to derive the changes in enthalpy and entropy, which arise from the cavity creation. The reversible work of cavity creation has a purely entropic origin as a consequence of the solvent-excluded volume effect produced by the inaccessibility of a region of the configurational space. The consequent structural reorganization leads to a perfect compensation of enthalpy and entropy changes. Such results are coherent with those obtained from Lee in his direct statistical mechanical study. [ABSTRACT FROM AUTHOR]

We study Einstein's gravity in AdS space coupled to nonlinear electrodynamics. Thermodynamics in extended phase space of magnetically charged black holes is investigated. We compute the metric and mass functions and their asymptotics, showing that black holes may have one or two horizons. The metric function is regular, f (0) = 1 , and corrections to the Reissner–Nordström solution are in the order of O (r − 3) when the Schwarzschild mass is zero. We prove that the first law of black hole thermodynamics and the generalized Smarr relation hold. The magnetic potential and vacuum polarization conjugated to coupling are computed and depicted. We calculate the Gibbs free energy and the heat capacity showing that first-order and second-order phase transitions take place. [ABSTRACT FROM AUTHOR]

A. Huxley's equations were used to determine the mechanical properties of muscle myosin II (MII) at the molecular level, as well as the probability of the occurrence of the different stages in the actin--myosin cycle. It was then possible to use the formalism of statistical mechanics with the grand canonical ensemble to calculate numerous thermodynamic parameters such as entropy, internal energy, affinity, thermodynamic flow, thermodynamic force, and entropy production rate. This allows us to compare the thermodynamic parameters of a non-muscle contractile system, such as the normal human placenta, with those of different striated skeletal muscles (soleus and extensor digitalis longus) as well as the heart muscle and smooth muscles (trachea and uterus) in the rat. In the human placental tissues, it was observed that the kinetics of the actin--myosin crossbridges were considerably slow compared with those of smooth and striated muscular systems. The entropy production rate was also particularly low in the human placental tissues, as compared with that observed in smooth and striated muscular systems. This is partly due to the low thermodynamic flow found in the human placental tissues. However, the unitary force of non-muscle myosin (NMII) generated by each crossbridge cycle in the myofibroblasts of the human placental tissues was similar in magnitude to that of MII in the myocytes of both smooth and striated muscle cells. Statistical mechanics represents a powerful tool for studying the thermodynamics of all contractile muscle and non-muscle systems. [ABSTRACT FROM AUTHOR]

Waste cooking oil's (WCO's) potential as a rejuvenator of aged asphalt has received attention in recent years, with the acid value of WCO affecting its rejuvenation effect. This study explored the rejuvenation effect of WCO with a high acid value on aged asphalt by using molecular dynamics simulation. First, the representative molecules of WCO with a high acid value and asphalt were determined. The rejuvenation effect of WCO on aged asphalt was analyzed by adding different contents of WCO to an aged asphalt model. The effect of WCO on the thermodynamic properties of the aged asphalt was analyzed. The results show that WCO can restore the thermodynamic properties of aged asphalt binder to a certain extent. Regarding the microstructure of rejuvenated asphalt, WCO molecules dispersed around asphaltenes weakened the latter's aggregation and improved the colloidal structure of the aged asphalt. In terms of interface adhesion properties, WCO can improve the adhesion properties between asphalt binder and SiO2, but it has limited influence on water sensitivity. The results allowed us to comprehensively evaluate the rejuvenation effect of WCO with a high acid value on aged asphalt and to explore its rejuvenation mechanism. [ABSTRACT FROM AUTHOR]

Favipiravir (FP) and ebselen (EB) belong to a diverse class of antiviral drugs known for their significant efficacy in treating various viral infections. Utilizing molecular dynamics (MD) simulations, machine learning, and van der Waals density functional theory, we accurately elucidate the binding properties of these antiviral drugs on a phosphorene single-layer. To further investigate these characteristics, this study employs four distinct machine learning models—Random Forest, Gradient Boosting, XGBoost, and CatBoost. The Hamiltonian of antiviral molecules within a monolayer of phosphorene is appropriately trained. The key aspect of utilizing machine learning (ML) in drug design revolves around training models that are efficient and precise in approximating density functional theory (DFT). Furthermore, the study employs SHAP (SHapley Additive exPlanations) to elucidate model predictions, providing insights into the contribution of each feature. To explore the interaction characteristics and thermodynamic properties of the hybrid drug, we employ molecular dynamics and DFT calculations in a vacuum interface. Our findings suggest that this functionalized 2D complex exhibits robust thermostability, indicating its potential as an effective and enabled entity. The observed variations in free energy at different surface charges and temperatures suggest the adsorption potential of FP and EB molecules from the surrounding environment. [ABSTRACT FROM AUTHOR]

We developed a macroscopic description of the evolutionary dynamics by following the temporal dynamics of the total Shannon entropy of sequences, denoted by S, and the average Hamming distance between them, denoted by H. We argue that a biological system can persist in the so-called quasi-equilibrium state for an extended period, characterized by strong correlations between S and H, before undergoing a phase transition to another quasi-equilibrium state. To demonstrate the results, we conducted a statistical analysis of SARS-CoV-2 data from the United Kingdom during the period between March 2020 and December 2023. From a purely theoretical perspective, this allowed us to systematically study various types of phase transitions described by a discontinuous change in the thermodynamic parameters. From a more-practical point of view, the analysis can be used, for example, as an early warning system for pandemics. [ABSTRACT FROM AUTHOR]

Small Li+Arn clusters are employed in this work as model systems to study microsolvation. Although first and second solvation shells are expected to be the most relevant ones for this type of atomic solvents, it is also interesting to explore larger clusters in order to identify the influence of external atoms on structural and thermodynamic properties. In this work, we perform a global geometry optimization for Li + Ar n clusters (with n = 41–100) and parallel tempering Monte Carlo (PTMC) simulations for some selected sizes. The results show that global minimum structures of large clusters always have 6 argon atoms in the first solvation shell while maintaining the number of 14 or 16 argon atoms in the second one. By contrast, third and fourth solvation shells vary significantly the number of argon atoms with the cluster size, and other shells can hardly be assigned due to the reduced influence of Li + on the external argon atoms for large clusters. In turn, PTMC calculations show that the melting of the most external solvation shells of large microsolvation clusters occurs at T ∼ 50 K , which is independent of cluster size. Structural transitions can be observed between quasi-degenerated structures at low temperatures. Moreover, the present results highlight the fluxional character of the external solvation shells of these large Li + Ar n clusters, which may be seen as typical "snowball" structures. [ABSTRACT FROM AUTHOR]

In this paper, by treating the cosmological constant as a thermodynamic pressure, we study the thermodynamics and phase transitions of the dyonic AdS black holes in Gauss-Bonnet-Scalar gravity, where the conformal scalar field is considered. In a more general extended phase space, we first verified the first law of black hole thermodynamics, and find that it is always true. Meanwhile, the corresponding Smarr relation is also obtained. Then, we found that this black hole exhibits interesting critical behaviors in six dimensions, i.e., two swallowtails can be observed simultaneously. Interestingly, in a specific parameter space, we observed the small/intermediate/large black hole phase transitions, with the triple point naturally appearing. Additionally, the small/large black hole phase transition, similar to the liquid/gas phase transition of the van der Waals fluids, can also be found in other parameter regions. Moreover, we note that the novel phase structure composed of two separate coexistence curves discovered in the dyonic AdS black holes in Einstein-Born-Infeld gravity disappears in Gauss-Bonnet-Scalar gravity. This suggests that this novel phase structure may be related to gravity theory, and importantly, it is generally observed that the triple point is a universal property of dyonic AdS black holes. On the other hand, we calculated the critical exponents near the critical points and found that they share the same values as in mean field theory. Finally, it is true that these results will provide some deep insights into the interesting thermodynamic properties of the dyonic AdS black holes in the background of conformal scalar fields. [ABSTRACT FROM AUTHOR]

Cluster expansion, which is a method that describes the concentration-dependent thermodynamic properties of materials while maintaining density functional theory accuracy, was used to predict new (CsPbIxBr1−x) structures. The cluster-expansion method generated 42 new stable (CsPb)xIyBrz (where x = 1 to 3 and y and z = 1 to 8) structures and these were ranked as meta-stable structures based on their enthalpies of formation. Monte Carlo calculations showed that CsPbI0.5Br0.5 composition separates into different phases at 300 K, but changes to a homogeneous phase at 700 K, suggesting that a different phase of CsPbI3 may exist at higher temperatures. Among the 42 predicted structures, randomly selected structures around iodide-rich, 50:50, and bromine-rich sites were studied further by determining their electronic, optical, mechanical, and thermodynamic properties using first-principle density functional theory. The materials possess similar properties as cubic Br-doped CsPbI3 perovskites. The mechanical properties of these compounds revealed that they are ductile in nature and mechanically stable. This work suggests that the introduction of impurities into CsPbI3 perovskite materials, as well as compositional engineering, can alter the electronic and optical properties, making them potential candidates for solar cell applications. [ABSTRACT FROM AUTHOR]

Classical thermodynamics employs the state of thermodynamic equilibrium, characterized by maximal disorder of the constituent particles, as the reference frame from which the Second Law is formulated and the definition of entropy is derived. Non-equilibrium thermodynamics analyzes the fluxes of matter and energy that are generated in the course of the general tendency to achieve equilibrium. The systems described by classical and non-equilibrium thermodynamics may be heuristically useful within certain limits, but epistemologically, they have fundamental problems in the application to autopoietic living systems. We discuss here the paradigm defined as a relational biological thermodynamics. The standard to which this refers relates to the biological function operating within the context of particular environment and not to the abstract state of thermodynamic equilibrium. This is defined as the stable non-equilibrium state, following Ervin Bauer. Similar to physics, where abandoning the absolute space-time resulted in the application of non-Euclidean geometry, relational biological thermodynamics leads to revealing the basic iterative structures that are formed as a consequence of the search for an optimal coordinate system by living organisms to maintain stable non-equilibrium. Through this search, the developing system achieves the condition of maximization of its power via synergistic effects. [ABSTRACT FROM AUTHOR]

In spirit of the recently proposed four-parameter generalized entropy of apparent horizon, we investigate inflationary cosmology where the matter field inside of the horizon is dominated by a scalar field with a power law potential (i.e., the form of ϕ n where ϕ is the scalar field under consideration). Actually without any matter inside of the horizon, the entropic cosmology leads to a de-Sitter spacetime, or equivalently, an eternal inflation with no exit. Thus in order to achieve a viable inflation, we consider a minimally coupled scalar field inside the horizon, and moreover, with the simplest quadratic potential. It is well known that the ϕ 2 potential in standard scalar field cosmology is ruled out from inflationary perspective as it is not consistent with the recent Planck 2018 data; (here it may be mentioned that in the realm of "apparent horizon thermodynamics", the standard scalar field cosmology is analogous to the case where the entropy of the apparent horizon is given by the Bekenstein–Hawking entropy). However, the story becomes different if the horizon entropy is of generalized entropic form, in which case, the effective energy density coming from the horizon entropy plays a significant role during the evolution of the universe. In particular, it turns out that in the context of generalized entropic cosmology, the ϕ 2 potential indeed leads to a viable inflation (according to the Planck data) with a graceful exit, and thus the potential can be made back in the scene. [ABSTRACT FROM AUTHOR]

We show that the configurational probability distribution of a classical gas always belongs to the q-exponential family. One of the consequences of this observation is that the thermodynamics of the configurational subsystem is uniquely determined up to a scaling function. As an example we consider a system of non-interacting harmonic oscillators. In this example, the scaling function can be determined from the requirement that in the limit of large systems the microcanonical temperature of the configurational subsystem should coincide with that of the canonical ensemble. The result suggests that Rényi's entropy function is the relevant one rather than that of Tsallis. [ABSTRACT FROM AUTHOR]

One can derive an analytic result for the issue of Bose–Einstein condensation (BEC) in anisotropic 2D harmonic traps. We find that the number of uncondensed bosons is represented by an analytic function, which includes a series expansion of q-digamma functions in mathematics. One can utilize this analytic result to evaluate various thermodynamic functions of ideal bosons in 2D anisotropic harmonic traps. The first major discovery is that the internal energy of a finite number of ideal bosons is a monotonically increasing function of anisotropy parameter p. The second major discovery is that, when p ≥ 0.5 , the changing with temperature of the heat capacity of a finite number of ideal bosons possesses the maximum value, which happens at critical temperature T c . The third major discovery is that, when 0.1 ≤ p < 0.5 , the changing with temperature of the heat capacity of a finite number of ideal bosons possesses an inflection point, but when p < 0.1 , the inflection point disappears. The fourth major discovery is that, in the thermodynamic limit, at T c and when p ≥ 0.5 , the heat capacity at constant number reveals a cusp singularity, which resembles the λ -transition of liquid helium-4. The fifth major discovery is that, in comparison to 2D isotropic harmonic traps ( p = 1 ), the singular peak of the specific heat becomes very gentle when p is lowered. [ABSTRACT FROM AUTHOR]

We studied Einstein's gravity with negative cosmological constant coupled to nonlinear electrodynamics proposed earlier. The metric and mass functions and corrections to the Reissner–Nordström solution are obtained. Black hole solutions can have one or two horizons. Thermodynamics and phase transitions of magnetically charged black holes in Anti-de Sitter spacetime are investigated. The first law of black hole thermodynamics is formulated and the generalized Smarr relation is proofed. By calculating the Gibbs free energy and heat capacity we study the black hole stability. Zero-order (reentrant), first-order, and second-order phase transitions are analyzed. The Joule–Thomson expansion is considered, showing the cooling and heating phase transitions. It was shown that the principles of causality and unitarity are satisfied in the model under consideration. [ABSTRACT FROM AUTHOR]

This paper presents an improved theoretical view of ab initio thermodynamics for polar GaN surfaces under gallium-rich conditions. The study uses density functional theory (DFT) calculations to systematically investigate the adsorption of gallium atoms on GaN polar surfaces, starting from the clean surface and progressing to the metallic multilayer. First principles phonon calculations are performed to determine vibrational free energies. Changes in the chemical potential of gallium adatoms are determined as a function of temperature and surface coverage. Three distinct ranges of Ga coverage with very low, medium, and high chemical potential are observed on the GaN(000-1) surface, while only two ranges with medium and high chemical potential are observed on the GaN(000-1) surface. The analysis confirms that a monolayer of Ga adatoms on the GaN(000-1) surface is highly stable over a wide range of temperatures. For a second adlayer at higher temperatures, it is energetically more favorable to form liquid droplets than a uniform crystalline adlayer. The second Ga layer on the GaN(0001) surface shows pseudo-crystalline properties even at a relatively high temperature. These results provide a better thermodynamic description of the surface state under conditions typical for molecular beam epitaxy and offer an interpretation of the observed growth window. [ABSTRACT FROM AUTHOR]

We review the main aspects of geometrothermodynamics, a formalism that uses contact geometry and Riemannian geometry to describe the properties of thermodynamic systems. We show how to handle in a geometric way the invariance of classical thermodynamics with respect to Legendre transformations, which means that the properties of the systems do not depend on the choice of the thermodynamic potential. Moreover, we show that, in geometrothermodynamics, it is possible to apply a variational principle to generate thermodynamic fundamental equations, which can be used in the context of relativistic cosmology to generate cosmological models. As a particular example, we consider a fundamental equation that relates the entropy with the internal energy and the volume of the Universe, and construct cosmological models with arbitrary parameters, which can be fixed to reproduce the main aspects of the inflationary era and the standard cosmological paradigm. [ABSTRACT FROM AUTHOR]

In the large coupling regime of the 5-dimensional Einstein--Maxwell--Chern--Simons theory, charged and rotating cohomogeneity-1 black holes form sequences of extremal and non-extremal radially excited configurations. These asymptotically global Anti-de Sitter (AdS5) black holes form a discrete set of solutions, characterised by the vanishing of the total angular momenta, or the horizon angular velocity. However, the solutions are not static. In this paper, we study the branch structure that contains these excited states, and its relation with the static Reissner--Nordström-AdS black hole. Thermodynamic properties of these solutions are considered, revealing that the branches with lower excitation number can become thermodynamically unstable beyond certain critical solutions that depend on the free parameters of the configuration. [ABSTRACT FROM AUTHOR]

Space plasmas are frequently described by kappa distributions. Non-extensive statistical mechanics involves the maximization of the Tsallis entropic form under the constraints of canonical ensemble, considering also a dyadic formalism between the ordinary and escort probability distributions. This paper addresses the statistical origin of kappa distributions, and shows that they can be connected with non-extensive statistical mechanics without considering the dyadic formalism of ordinary/escort distributions. While this concept does significantly simplify the usage of the theory, it costs the definition of a dyadic entropic formulation, in order to preserve the consistency between statistical mechanics and thermodynamics. Therefore, the simplification of the theory by means of avoiding dyadic formalism is impossible within the framework of non-extensive statistical mechanics. [ABSTRACT FROM AUTHOR]

We investigated two different approaches, which can be used to extend the standard quantum statistical mechanics. One is based on fractional calculus, and the other considers the extension of the concept of entropy, i.e., the Tsallis statistics. We reviewed and discussed some of the main properties of these approaches and used the thermal Green function formalism to perform the developments, simultaneously allowing us to analyze each case's dynamics and thermodynamics aspects. In particular, the results allow us to understand how the extensions change the behavior of some quantities, particularly fluctuations related to the system. [ABSTRACT FROM AUTHOR]

Favipiravir (FP) and Ebselen (EB) belong to a broad range of antiviral drugs that have shown active potential as medications against many viruses. Employing molecular dynamics simulations and machine learning (ML) combined with van der Waals density functional theory, we have uncovered the binding characteristics of these two antiviral drugs on a phosphorene nanocarrier. Herein, by using four different machine learning models (i.e., Bagged Trees, Gaussian Process Regression (GPR), Support Vector Regression (SVR), and Regression Trees (RT)), the Hamiltonian and the interaction energy of antiviral molecules in a phosphorene monolayer are trained in an appropriate way. However, training efficient and accurate models for approximating the density functional theory (DFT) is the final step in using ML to aid in the design of new drugs. To improve the prediction accuracy, the Bayesian optimization approach has been employed to optimize the GPR, SVR, RT, and BT models. Results revealed that the GPR model obtained superior prediction performance with an R 2 of 0.9649, indicating that it can explain 96.49% of the data's variability. Then, by means of DFT calculations, we examine the interaction characteristics and thermodynamic properties in a vacuum and a continuum solvent interface. These results illustrate that the hybrid drug is an enabled, functionalized 2D complex with vigorous thermostability. The change in Gibbs free energy at different surface charges and temperatures implies that the FP and EB molecules are allowed to adsorb from the gas phase onto the 2D monolayer at different pH conditions and high temperatures. The results reveal a valuable antiviral drug therapy loaded by 2D biomaterials that may possibly open a new way of auto-treating different diseases, such as SARS-CoV, in primary terms. [ABSTRACT FROM AUTHOR]

Polyelectrolyte has wide applications in biomedicine, agriculture and soft robotics. However, it is among one of the least understood physical systems because of the complex interplay of electrostatics and polymer nature. In this review, a comprehensive description is presented on experimental and theoretical studies of the activity coefficient, one of the most important thermodynamic properties of polyelectrolyte. Experimental methods to measure the activity coefficient were introduced, including direct potentiometric measurement and indirect methods such as isopiestic measurement and solubility measurement. Next, progress on the various theoretical approaches was presented, ranging from analytical, empirical and simulation methods. Finally, challenges for future development are proposed on this field. [ABSTRACT FROM AUTHOR]

Adopted by the Intergovernmental Oceanographic Commission (IOC) of UNESCO in 2010 and the International Union of Geodesy and Geophysics (IUGG) in 2011, the Thermodynamic Equation of Seawater 2010 (TEOS-10) is the current geophysical standard for the thermodynamic properties of humid air, seawater and ice. TEOS-10 equations for evaporation and sublimation enthalpies are derived mathematically from the thermodynamic potential of a »sea air« model, denoting a multi-phase equilibrium composite of the geophysical aqueous mixtures. To estimating evaporation rates from the ocean, Dalton equations in various versions are implemented in numerical climate models. Some of those equations appear to be biased on climatic time scales if compared with proper thermodynamic driving forces. Such equations may lead to a spurious amplification of the hydrological cycle and an implied effect of cooling oceans. As an unbiased alternative, Dalton equations are proposed in terms of TEOS-10 relative fugacity (RF) or its conventional relative humidity (RH) approximations. With respect to RH uncertainties or trends, the substantial sensitivity of the evaporation flux may be estimated to be as much as 5 W m−2 per 1 %rh. Within a maximum error of only 0.04 %rh, sea-surface RF may be approximated in terms of dew-point or frost-point temperatures using a simple formula. [ABSTRACT FROM AUTHOR]

Metadynamics calculations of large chemical systems with ab initio methods are computationally prohibitive due to the extensive sampling required to simulate the large degrees of freedom in these systems. To address this computational bottleneck, we utilized a GPU-enhanced density functional tight binding (DFTB) approach on a massively parallelized cloud computing platform to efficiently calculate the thermodynamics and metadynamics of biochemical systems. To first validate our approach, we calculated the free-energy surfaces of alanine dipeptide and showed that our GPU-enhanced DFTB calculations qualitatively agree with computationally-intensive hybrid DFT benchmarks, whereas classical force fields give significant errors. Most importantly, we show that our GPU-accelerated DFTB calculations are significantly faster than previous approaches by up to two orders of magnitude. To further extend our GPU-enhanced DFTB approach, we also carried out a 10 ns metadynamics simulation of remdesivir, which is prohibitively out of reach for routine DFT-based metadynamics calculations. We find that the free-energy surfaces of remdesivir obtained from DFTB and classical force fields differ significantly, where the latter overestimates the internal energy contribution of high free-energy states. Taken together, our benchmark tests, analyses, and extensions to large biochemical systems highlight the use of GPU-enhanced DFTB simulations for efficiently predicting the free-energy surfaces/thermodynamics of large biochemical systems. [ABSTRACT FROM AUTHOR]

In this work, we study the thermodynamics of a hybrid system based on the Da Providencia–Schütte Hamiltonian. The model consists of bosons, i.e., photons in a cavity, interacting with an ensemble of spins through a pseudo-Hermitian Hamiltonian. We compute the exact partition function of the system, and from it, we derive the statistical properties of the system. Finally, we evaluate the work that can be extracted from the system by performing an Otto cycle and discuss the advantages of the proposed pseudo-Hermitian interaction. [ABSTRACT FROM AUTHOR]

A theoretical-computational procedure based on the quasi-Gaussian entropy (QGE) theory and molecular dynamics (MD) simulations is proposed for the calculation of thermodynamic properties for molecular and supra-molecular species in the gas phase. The peculiarity of the methodology reported in this study is its ability to construct an analytical model of all the most relevant thermodynamic properties, even within a wide temperature range, based on a practically automatic sampling of the entire conformational repertoire of highly flexible systems, thereby bypassing the need for an explicit search for all possible conformers/rotamers deemed relevant. In this respect, the reliability of the presented method mainly depends on the quality of the force field used in the MD simulations and on the ability to discriminate in a physically coherent way between semi-classical and quantum degrees of freedom. The method was tested on six model systems (n-butane, n-butane, n-octanol, octadecane, 1-butyl-3-methylimidazolium hexafluorophosphate and 1-butyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide ionic pairs), which, being experimentally characterized and already addressed by other theoretical-computational methods, were considered as particularly suitable to allow us to evaluate the method's accuracy and efficiency, bringing out advantages and possible drawbacks. The results demonstrate that such a physically coherent yet relatively simple method can represent a further valid computational tool that is alternative and complementary to other extremely efficient computational methods, as it is particularly suited for addressing the thermodynamics of gaseous systems with a high conformational complexity over a large range of temperature. [ABSTRACT FROM AUTHOR]

In this review, motivated by the recent interest in high-temperature materials, we review our recent progress in theories of lattice dynamics in and out of equilibrium. To investigate thermodynamic properties of anharmonic crystals, the self-consistent phonon theory was developed, mainly in the 1960s, for rare gas atoms and quantum crystals. We have extended this theory to investigate the properties of the equilibrium state of a crystal, including its unit cell shape and size, atomic positions and lattice dynamical properties. Using the equation-of-motion method combined with the fluctuation–dissipation theorem and the Donsker–Furutsu–Novikov (DFN) theorem, this approach was also extended to investigate the non-equilibrium case where there is heat flow across a junction or an interface. The formalism is a classical one and therefore valid at high temperatures. [ABSTRACT FROM AUTHOR]

Cocrystals of Active Pharmaceutical Ingredients (APIs) are an attractive therapeutic alternative to salt formations. However, due to the molecular scale processes involved, the earliest stages of cocrystal formation remain poorly understood. In this paper, some light is shed on the thermodynamics and kinetics of co-crystallization. Importantly, to mimic the molecular scale processes of cocrystal formation, we use 2D Monte Carlo simulations and a computational model with short-range attraction and a mixture of two types of patchy particles (PPs) monomers. Each type possesses four patches, grouped in two by two, and each couple of patches is characterized by its specific placement on the circumference of the monomer and corresponding patch strength (a strong and narrow or weak and wide interaction). The spatial placement of the patches on both PPs monomers (alternating periodically through 60 and 120 degrees and vice versa) selected by us shows the emergence of both rhombohedral (metastable) and trihexagonal (stable) Kagome-like structures. The Kagome-like structures are preceded by formation of two types of trimers involving strong bonds only, or mixed trimers of strong and weak bonds, the later serving as building blocks for the finally generated Kagome patchy cocrystal, after prolonged simulation times. The step-by step process governing the cocrystal formation is discussed in detail, concerning the temperature interval, concentrations of PPs, the specific patch geometry and patch anisotropy as well. It is to be hoped that an understanding of the mechanisms of co-crystallization can help to control practical cocrystal synthesis and the possible phase transformations. [ABSTRACT FROM AUTHOR]

We consider a system of Brownian particles with long-range interactions. We go beyond the mean field approximation and take fluctuations into account. We introduce a new class of stochastic Fokker-Planck equations associated with a generalized thermodynamical formalism. Generalized thermodynamics arises in the case of complex systems experiencing small-scale constraints. In the limit of short-range interactions, we obtain a generalized class of stochastic Cahn-Hilliard equations. Our formalism has application for several systems of physical interest including self-gravitating Brownian particles, colloid particles at a fluid interface, superconductors of type II, nucleation, the chemotaxis of bacterial populations, and two-dimensional turbulence. We also introduce a new type of generalized entropy taking into account anomalous diffusion and exclusion or inclusion constraints. [ABSTRACT FROM AUTHOR]

We compare and contrast three different, but complementary views of "structure" and "pattern" in spatial processes. For definiteness and analytical clarity, we apply all three approaches to the simplest class of spatial processes: one-dimensional Ising spin systems with finite-range interactions. These noncritical systems are well-suited for this study since the change in structure as a function of system parameters is more subtle than that found in critical systems where, at a phase transition, many observables diverge, thereby making the detection of change in structure obvious. This survey demonstrates that the measures of pattern from information theory and computational mechanics differ from known thermodynamic and statistical mechanical functions. Moreover, they capture important structural features that are otherwise missed. In particular, a type of mutual information called the excess entropy—an information theoretic measure of memory—serves to detect ordered, low entropy density patterns. It is superior in several respects to other functions used to probe structure, such as magnetization and structure factors. ϵ -Machines—the main objects of computational mechanics—are seen to be the most direct approach to revealing the (group and semigroup) symmetries possessed by the spatial patterns and to estimating the minimum amount of memory required to reproduce the configuration ensemble, a quantity known as the statistical complexity. Finally, we argue that the information theoretic and computational mechanical analyses of spatial patterns capture the intrinsic computational capabilities embedded in spin systems—how they store, transmit, and manipulate configurational information to produce spatial structure. [ABSTRACT FROM AUTHOR]

The π–π interaction is a major driving force that stabilizes protein assemblies during protein folding. Recent studies have additionally demonstrated its involvement in the liquid–liquid phase separation (LLPS) of intrinsically disordered proteins (IDPs). As the participating residues in IDPs are exposed to water, π–π interactions for LLPS must be modeled in water, as opposed to the interactions that are often established at the hydrophobic domains of folded proteins. Thus, we investigated the association of free energies of benzene and phenol dimers in water by integrating van der Waals (vdW)-corrected density functional theory (DFT) and DFT in classical explicit solvents (DFT-CES). By comparing the vdW-corrected DFT and DFT-CES results with high-level wavefunction calculations and experimental solvation free energies, respectively, we established the quantitative credibility of these approaches, enabling a reliable prediction of the benzene and phenol dimer association free energies in water. We discovered that solvation influences dimer association free energies, but not significantly when no direct hydrogen-bond-type interaction exists between two monomeric units, which can be explained by the enthalpy–entropy compensation. Our comprehensive computational study of the solvation effect on π–π interactions in water could help us understand the molecular-level driving mechanism underlying the IDP phase behaviors. [ABSTRACT FROM AUTHOR]

The thermodynamics and phase transitions of magnetic Anti-de Sitter black holes were studied. We considered extended-phase-space thermodynamics, with the cosmological constant being a thermodynamic pressure and the black hole mass being treated as a chemical enthalpy. The extended-phase-space thermodynamics of black holes mimic the behavior of a Van der Waals liquid. Quantities conjugated to the coupling of nonlinear electrodynamics (NED) and a magnetic charge are obtained. Thermodynamic critical points of phase transitions are investigated. It was demonstrated that the first law of black hole thermodynamics and the generalized Smarr relation hold. The Joule–Thomson adiabatic expansion of NED-AdS black holes is studied. The dependence of inversion temperature on pressure and the minimum of the inversion temperature are found. [ABSTRACT FROM AUTHOR]

Kirkwood–Buff Integral (KBI) theory is an important method for the analysis of the structural and thermodynamic properties of liquid solutions. For solids, the calculation of KBIs has become possible only recently through the finite-volume generalisation of KBI theory, but it has so far only been applied to monoatomic crystals. Here, we show that KBI theory can be applied to solid mixtures and compute the KBIs of a Ar x Xe 1 − x solid solution, for 0 < x < 0.1 and temperature T = 84 − 86 K, from pair distribution functions obtained by Monte Carlo simulation. From the KBIs, the isothermal compressibility, partial molar volumes, and thermodynamic factors are calculated and found to be in good agreement with alternative theoretical methods. The analysis of the KBIs and the partial molar volumes give insight into the structure of the mixture. The KBI of Ar pairs is much larger than that of Xe pairs, which indicates the tendency of Ar impurities to accumulate. The evolution of the partial molar volumes with increasing Ar molar fraction x shows a transition at x ≈ 0.06 , which reflects the formation of Ar clusters, precursors of the Ar-rich liquid phase. The calculated thermodynamic factors show that the solid(Xe) phase becomes unstable at x ≈ 0.1 , indicating the start of the solid (Xe)–liquid (Ar) equilibrium. The chemical potentials of Ar and Xe are obtained from the thermodynamic factor by integration over ln x , and by fitting the data to the Margules equations, the activity coefficients can be estimated over the whole composition range. The present findings extend the domain of applicability of the KBI solution theory from liquids to solids. [ABSTRACT FROM AUTHOR]

Computational simulation of colloidal systems make use of empirical interaction potentials that are founded in well-established theory. In this work, we have performed parallel tempering Monte Carlo (PTMC) simulations to calculate heat capacity and to assess structural transitions, which may occur in charged colloidal clusters whose effective interactions are described by a sum of pair potentials with attractive short-range and repulsive long-range components. Previous studies on these systems have shown that the global minimum structure varies from spherical-type shapes for small-size clusters to Bernal spiral and "beaded-necklace" shapes at intermediate and larger sizes, respectively. In order to study both structural transitions and dissociation, we have organized the structures appearing in the PTMC calculations by three sets according to their energy: (i) low-energy structures, including the global minimum; (ii) intermediate-energy "beaded-necklace" motifs; (iii) high-energy linear and branched structures that characterize the dissociative clusters. We observe that, depending on the cluster, either peaks or shoulders on the heat–capacity curve constitute thermodynamics signatures of dissociation and structural transitions. The dissociation occurs at T = 0.20 for all studied clusters and it is characterized by the appearance of a significant number of linear structures, while the structural transitions corresponding to unrolling the Bernal spiral are quite dependent on the size of the colloidal system. [ABSTRACT FROM AUTHOR]

Many methods to produce hydrate reservoirs have been proposed in the last three decades. Thermal stimulation and injection of thermodynamic hydrate inhibitors are just two examples of methods which have seen reduced attention due to their high cost. However, different methods for producing hydrates are not evaluated thermodynamically prior to planning expensive experiments or pilot tests. This can be due to lack of a thermodynamic toolbox for the purpose. Another challenge is the lack of focus on the limitations of the hydrate phase transition itself. The interface between hydrate and liquid water is a kinetic bottle neck. Reducing pressure does not address this problem. An injection of CO2 will lead to the formation of a new CO2 hydrate. This hydrate formation is an efficient heat source for dissociating hydrate since heating breaks the hydrogen bonds, directly addressing the problem of nano scale kinetic limitation. Adding limited amounts of N2 increases the permeability of the injection gas. The addition of surfactant increases gas/water interface dynamics and promotes heterogeneous hydrate formation. In this work we demonstrate a residual thermodynamic scheme that allows thermodynamic analysis of different routes for hydrate formation and dissociation. We demonstrate that 20 moles per N2 added to the CO2 is thermodynamically feasible for generating a new hydrate into the pores. When N2 is added, the available hydrate formation enthalpy is reduced as compared to pure CO2, but is still considered sufficient. Up to 3 mole percent ethanol in the free pore water is also thermodynamically feasible. The addition of alcohol will not greatly disturb the ability to form new hydrate from the injection gas. Homogeneous hydrate formation from dissolved CH4 and/or CO2 is limited in amount and not important. However, the hydrate stability limits related to concentration of hydrate former in surrounding water are important. Mineral surfaces can act as hydrate promotors through direct adsorption, or adsorption in water that is structured by mineral surface charges. These aspects will be quantified in a follow-up paper, along with kinetic modelling based on thermodynamic modelling in this work. [ABSTRACT FROM AUTHOR]

In nonadditive systems, like small systems or like long-range interacting systems even in the thermodynamic limit, ensemble inequivalence can be related to the occurrence of negative response functions, this in turn being connected with anomalous concavity properties of the thermodynamic potentials associated with the various ensembles. We show how the type and number of negative response functions depend on which of the quantities E, V and N (energy, volume and number of particles) are constrained in the ensemble. In particular, we consider the unconstrained ensemble in which E, V and N fluctuate, which is physically meaningful only for nonadditive systems. In fact, its partition function is associated with the replica energy, a thermodynamic function that identically vanishes when additivity holds, but that contains relevant information in nonadditive systems. [ABSTRACT FROM AUTHOR]

The Gibbs paradox in statistical mechanics is often taken to indicate that already in the classical domain particles should be treated as fundamentally indistinguishable. This paper shows, on the contrary, how one can recover the thermodynamical account of the entropy of mixing, while treating states that only differ by permutations of similar particles as distinct. By reference to the orthodox theory of thermodynamics, it is argued that entropy differences are only meaningful if they are related to reversible processes connecting the initial and final state. For mixing processes, this means that processes should be considered in which particle number is allowed to vary. Within the context of statistical mechanics, the Gibbsian grandcanonical ensemble is a suitable device for describing such processes. It is shown how the grandcanonical entropy relates in the appropriate way to changes of other thermodynamical quantities in reversible processes, and how the thermodynamical account of the entropy of mixing is recovered even when treating the particles as distinguishable. [ABSTRACT FROM AUTHOR]