Search

The conversion of biomass to 5-hydroxymethylfurfural (HMF) holds substantial promise as a renewable energy source. Notably, HMF can be transformed into 2,5-bis(hydroxymethyl)furan (BHMF), a crucial reactant in biofuel production, but requires harsh operating conditions, H2, and precious metal catalysts. A recently reported Cannizzaro reaction of HMF to BHMF, characterized by its efficiency, mild conditions, and eco-friendliness, instead employed ionic liquids (ILs) to achieve high yields. In this study, combined quantum mechanical and molecular mechanical (QM/MM) simulations in conjunction with Metropolis Monte Carlo statistical mechanics and free-energy perturbation theory utilized M06-2X/6-31+G(d), PDDG/PM3, and the OPLS-VSIL force field to uncover important solute–solvent interactions present in the HMF to BHMF reaction pathway. The Cannizzaro reaction was examined in water and in five ILs composed of the 1-butyl-3-methylimidazolium [BMIM] cation coupled to hexafluorophosphate, tetrafluoroborate, thiocyanate, chloride, and bromide. Energetic and structural analysis of the rate-determining hydride transfer between HMF and the hydride-donor anion HMFOH− attributed the enhanced reactivity to highly organized solvent interactions featuring (1) hydrogen bonding between the ring protons of [BMIM] and the negatively charged carbonyl oxygen atoms on the transition structure, (2) favorable electrostatic interactions between the IL anions and solute hydroxyl groups, and (3) beneficial π–π stacking interactions between [BMIM] and the two aromatic rings present in HMF and HMFOH−. [ABSTRACT FROM AUTHOR]

Theories of small systems play an important role in the fundamental understanding of finite size effects in statistical mechanics, as well as the validation of molecular simulation results as no computer can simulate fluids in the thermodynamic limit. Previously, a shell particle was included in the isothermal–isobaric ensemble in order to resolve an ambiguity in the resulting partition function. The shell particle removed either redundant volume states or redundant translational degrees of freedom of the system and yielded quantitative differences from traditional simulations in this ensemble. In this work, we investigate the effect of including a shell particle in the canonical, grand canonical, and Gibbs ensembles. For systems comprised of a pure component ideal gas, analytical expressions for various thermodynamic properties are obtained. We also derive the Metropolis Monte Carlo simulation acceptance criteria for these ensembles with shell particles, and the results of the simulations of an ideal gas are in excellent agreement with the theoretical predictions. The system size dependence of various important ensemble averages is also analyzed. [ABSTRACT FROM AUTHOR]

A summary of the development of Monte Carlo statistical mechanics simulations for the computation of free energies of hydration of organic molecules is followed by presentation of results with the latest version of the optimized potentials for liquid simulations–all atom force field and the TIP4P water model. Scaling of the Lennard-Jones interactions between water, oxygen, and carbon atoms by a factor of 1.25 is found to improve the accuracy of free energies of hydration for 50 prototypical organic molecules from a mean unsigned error of 1.0–1.2 to 0.4 kcal/mol. [ABSTRACT FROM AUTHOR]

The potential energy landscape (PEL) formalism is a tool within statistical mechanics that has been used in the past to calculate the equation of states (EOS) of classical rigid model liquids at low temperatures, where computer simulations may be challenging. In this work, we use classical molecular dynamics (MD) simulations and the PEL formalism to calculate the EOS of the flexible q-TIP4P/F water model. This model exhibits a liquid–liquid critical point (LLCP) in the supercooled regime, at (Pc = 150 MPa, Tc = 190 K, and ρc = 1.04 g/cm3) [using the reaction field technique]. The PEL-EOS of q-TIP4P/F water and the corresponding location of the LLCP are in very good agreement with the MD simulations. We show that the PEL of q-TIP4P/F water is Gaussian, which allows us to calculate the configurational entropy of the system, Sconf. The Sconf of q-TIP4P/F water is surprisingly similar to that reported previously for rigid water models, suggesting that intramolecular flexibility does not necessarily add roughness to the PEL. We also show that the Adam–Gibbs relation, which relates the diffusion coefficient D with Sconf, holds for the flexible q-TIP4P/F water model. Overall, our results indicate that the PEL formalism can be used to study molecular systems that include molecular flexibility, the common case in standard force fields. This is not trivial since the introduction of large bending/stretching mode frequencies is problematic in classical statistical mechanics. For example, as shown previously, we find that such high frequencies lead to unphysical (negative) entropy for q-TIP4P/F water when using classical statistical mechanics (yet, the PEL formalism can be applied successfully). [ABSTRACT FROM AUTHOR]

Henchman's approximate harmonic model of liquids is extended to predict the thermodynamic behavior along lines of constant excess entropy ("isomorphs") in the liquid and supercritical fluid regimes of the Lennard-Jones (LJ) potential phase diagram. Simple analytic expressions based on harmonic cell models of fluids are derived for the isomorph lines, one accurate version of which only requires as input parameters the average repulsive and attractive parts of the potential energy per particle at a single reference state point on the isomorph. The new harmonic cell routes for generating the isomorph lines are compared with those predicted by the literature molecular dynamics (MD) methods, the small step MD method giving typically the best agreement over a wide density and temperature range. Four routes to calculate the excess entropy in the MD simulations are compared, which includes employing Henchman's formulation, Widom's particle insertion method, thermodynamic integration, and parameterized LJ equations of state. The thermodynamic integration method proves to be the most computationally efficient. The excess entropy is resolved into contributions from the repulsive and attractive parts of the potential. The repulsive and attractive components of the potential energy, excess Helmholtz free energy, and excess entropy along a fluid isomorph are predicted to vary as ∼T−1/2 in the high temperature limit by an extension of classical inverse power potential perturbation theory statistical mechanics, trends that are confirmed by the MD simulations. [ABSTRACT FROM AUTHOR]

Coarse-graining of fluids is challenging because fluid particles are unbound and diffuse long distances in time. One approach creates coarse-grain variables that group all particles within a region centered on specific points in space and accounts for the movement of particles among such regions. In our previous work, we showed that in many cases, potential interactions for such a scheme adopted a generalized quadratic form, whose parameters depend on means, variances, and correlation coefficients among the coarse-grain variables. In this work, we use statistical mechanics to derive analytic expressions for these parameters, using properties of the fluid, including pair distribution functions. These expressions are compared against simulation-derived values and shown to be in good agreement. This approach can be used to calculate a priori the potential for any homogeneous, simple fluid, without the need for fitting procedures or matching, thus increasing the ease of use of this coarse-grain scheme and creating a foundation for large-scale bottom-up simulations. Furthermore, these expressions provide a quantitative way of studying the boundary between discrete (atomic) and continuum models of fluids. [ABSTRACT FROM AUTHOR]

The swift progression and expansion of machine learning (ML) have not gone unnoticed within the realm of statistical mechanics. In particular, ML techniques have attracted attention by the classical density-functional theory (DFT) community, as they enable automatic discovery of free-energy functionals to determine the equilibrium-density profile of a many-particle system. Within classical DFT, the external potential accounts for the interaction of the many-particle system with an external field, thus, affecting the density distribution. In this context, we introduce a statistical-learning framework to infer the external potential exerted on a classical many-particle system. We combine a Bayesian inference approach with the classical DFT apparatus to reconstruct the external potential, yielding a probabilistic description of the external-potential functional form with inherent uncertainty quantification. Our framework is exemplified with a grand-canonical one-dimensional classical particle ensemble with excluded volume interactions in a confined geometry. The required training dataset is generated using a Monte Carlo (MC) simulation where the external potential is applied to the grand-canonical ensemble. The resulting particle coordinates from the MC simulation are fed into the learning framework to uncover the external potential. This eventually allows us to characterize the equilibrium density profile of the system by using the tools of DFT. Our approach benchmarks the inferred density against the exact one calculated through the DFT formulation with the true external potential. The proposed Bayesian procedure accurately infers the external potential and the density profile. We also highlight the external-potential uncertainty quantification conditioned on the amount of available simulated data. The seemingly simple case study introduced in this work might serve as a prototype for studying a wide variety of applications, including adsorption, wetting, and capillarity, to name a few. [ABSTRACT FROM AUTHOR]

A first theoretical attempt is made to understand the characteristics of dust acoustic shock waves (DASWs) in a polarized electron-depleted plasma with a mixed nonextensive high energy–tail ion distribution and to examine the impact of the generalized nonthermal polarization force on DASWs in an electron-depleted dusty plasma. First, a short numerical investigation illustrating the behavior of the mixed nonextensive high energy–tail (or Cairns–Tsallis) ion distribution and the domain of validity of its two parameters (q and α) is carried out. Next, the generalized nonthermal polarization acting on dust grain in electron-depleted dusty plasma is determined within the context of Tsallis' statistical mechanics. The behavior of this generalized polarization force is significantly affected by the nonextensive character of the nonthermal ions. Specifically, we have shown that, for both space and experimental dusty plasmas, the magnitude of the polarization force (in the case where − 1 < q < 1) decreases as the nonextensivity of the nonthermal ions becomes significant. As an application, we have analyzed the changes caused by the nonthermal nonextensive polarization force on the main characteristics of DASW (viz. phase velocity, polarity, amplitude, width, etc.). Numerical results showed that our plasma model supports rarefactive and compressive DASWs that are significantly affected by the effects of nonthermal ion nonextensivity and polarization force. In particular, we have shown that for large values of the nonthermal parameter α , the increase in q allows the transition from rarefactive to compressive DASW structures. The present theoretical investigation is helpful to fully understand electrostatic disturbances in space and experimental dusty plasmas. [ABSTRACT FROM AUTHOR]

The principles of ergodicity and thermalization constitute the foundation of statistical mechanics, positing that a many-body system progressively loses its local information as it evolves. Nevertheless, these principles can be disrupted when thermalization dynamics lead to the conservation of local information, as observed in the phenomenon known as many-body localization. Quantum spin chains provide a fundamental platform for exploring the dynamics of closed interacting quantum many-body systems. This study explores the dynamics of a spin chain with S ≥ 1 / 2 within the incorporating a non-uniform magnetic field and single-ion anisotropy. Through the use of exact numerical diagonalization, we unveil that a nearly constant-gradient magnetic field suppresses thermalization, a phenomenon termed Stark many-body localization (SMBL), previously observed in S = 1 / 2 chains. Furthermore, our findings reveal that the sole presence of single-ion anisotropy is sufficient to prevent thermalization in the system. Interestingly, when the magnitudes of the magnetic field and anisotropy are comparable, they compete, favoring delocalization. Despite the potential hindrance of SMBL by single-ion anisotropy in this scenario, it introduces an alternative mechanism for localization. Our interpretation, considering local energetic constraints and resonances between degenerate eigenstates, not only provides insights into SMBL but also opens avenues for future experimental investigations into the enriched phenomenology of disordered free localized S ≥ 1 / 2 systems. [ABSTRACT FROM AUTHOR]

Sulfate dry-wet cycle erosion significantly affects the mechanical properties of concrete. Investigating the uniaxial compressive stress-strain relationship under these conditions is essential for developing accurate constitutive models. This study analyzes the uniaxial stress-strain curves of concrete subjected to dry-wet cycles in 5% and 15% sulfate solutions. The results show that the initial compaction phase in the stress-strain relationship is particularly pronounced under increasing sulfate concentrations and cycle counts. The concrete experiences an extended compaction phase, which accounts for up to 35.71% of the total strain process. This finding challenge traditional constitutive models, which struggle to accurately describe this phase. To address this issue, the study develops a nonlinear stress-strain model for concrete, incorporating the initial damage caused by sulfate dry-wet cycle erosion, based on Weibull statistical damage mechanics principles. The research indicates that the effects of sulfate concentration and cycle count are predominantly reflected in the pronounced nonlinearity of the skeleton strain function's opening size (a) and shape characteristics (b), modeled using a fourth-degree polynomial. The model demonstrates an excellent fit to experimental data with an R2 value of 0.99989, showing that the proposed nonlinear stress-strain relationship effectively captures the uniaxial mechanical behavior of concrete under sulfate dry-wet cycle erosion and provides a robust framework for developing constitutive models in such environments. [ABSTRACT FROM AUTHOR]

This study introduces the long‐range Ising model from statistical mechanics to the performance‐based earthquake engineering (PBEE) framework for regional seismic damage analysis. The application of the PBEE framework at a regional scale involves estimating the damage states (DSs$DS\mathrm{s}$) of numerous structures, typically performed using fragility function‐based stochastic simulations. However, these simulations often assume conditional independence or employ simplistic dependency models among the DSs$DS\mathrm{s}$ of structures, leading to significant misrepresentation of regional risk. The Ising model addresses this issue by converting the available information on binary DSs$DS\mathrm{s}$ (safe or failure) into a joint probability mass function, leveraging the principle of maximum entropy. The Ising model offers two main benefits: (1) it requires only the first‐ and second‐order cross‐moments, enabling seamless integration with the existing PBEE framework, and (2) it provides meaningful physical interpretations of the model parameters, facilitating the uncovering of insights not apparent from data. To demonstrate the proposed method, we applied the Ising model to 156 buildings in Antakya, Turkey, using post‐hazard damage evaluation data, and to 182 buildings in Pacific Heights, San Francisco, using simulated data from the Regional Resilience Determination tool. In both instances, the Ising model accurately reproduces the provided information and generates meaningful insights into regional damage. The study also investigates the change in Ising model parameters under varying earthquake magnitudes, along with the mean‐field approximation, further facilitating the applicability of the proposed approach. [ABSTRACT FROM AUTHOR]

In this review work, we outline a conceptual path that, starting from the numerical investigation of the transition between weak chaos and strong chaos in Hamiltonian systems with many degrees of freedom, comes to highlight how, at the basis of equilibrium phase transitions, there must be major changes in the topology of submanifolds of the phase space of Hamiltonian systems that describe systems that exhibit phase transitions. In fact, the numerical investigation of Hamiltonian flows of a large number of degrees of freedom that undergo a thermodynamic phase transition has revealed peculiar dynamical signatures detected through the energy dependence of the largest Lyapunov exponent, that is, of the degree of chaoticity of the dynamics at the phase transition point. The geometrization of Hamiltonian flows in terms of geodesic flows on suitably defined Riemannian manifolds, used to explain the origin of deterministic chaos, combined with the investigation of the dynamical counterpart of phase transitions unveils peculiar geometrical changes of the mechanical manifolds in correspondence to the peculiar dynamical changes at the phase transition point. Then, it turns out that these peculiar geometrical changes are the effect of deeper topological changes of the configuration space hypersurfaces  ∑ v = V N − 1 (v)  as well as of the manifolds  { M v = V N − 1 ((− ∞ , v ]) } v ∈ R  bounded by the ∑v. In other words, denoting by vc the critical value of the average potential energy density at which the phase transition takes place, the members of the family  { ∑ v } v < v c  are not diffeomorphic to those of the family  { ∑ v } v > v c ; additionally, the members of the family  { M v } v > v c  are not diffeomorphic to those of  { M v } v > v c . The topological theory of the deep origin of phase transitions allows a unifying framework to tackle phase transitions that may or may not be due to a symmetry-breaking phenomenon (that is, with or without an order parameter) and to finite/small N systems. [ABSTRACT FROM AUTHOR]

In this work, we study the time-dependent behavior of quantum correlations of a system of an inverted oscillator governed by out-of-equilibrium dynamics using the well-known Schwinger–Keldysh formalism in the presence of quantum mechanical quench. Considering a generalized structure of a time-dependent Hamiltonian for an inverted oscillator system, we use the invariant operator method to obtain its eigenstate and continuous energy eigenvalues. Using the expression for the eigenstate, we further derive the most general expression for the generating function as well as the out-of-time-ordered correlators (OTOCs) for the given system using this formalism. Further, considering the time-dependent coupling and frequency of the quantum inverted oscillator characterized by quench parameters, we comment on the dynamical behavior, specifically the early, intermediate and late time-dependent features of the OTOC for the quenched quantum inverted oscillator. Next, we study a specific case, where the system of an inverted oscillator exhibits chaotic behavior by computing the quantum Lyapunov exponent from the time-dependent behavior of OTOCs in the presence of the given quench profile. [ABSTRACT FROM AUTHOR]

Interactions among the underlying agents of a complex system are not only limited to dyads but can also occur in larger groups. Currently, no generic model has been developed to capture high-order interactions (HOI), which, along with pairwise interactions, portray a detailed landscape of complex systems. Here, we integrate evolutionary game theory and behavioral ecology into a unified statistical mechanics framework, allowing all agents (modeled as nodes) and their bidirectional, signed, and weighted interactions at various orders (modeled as links or hyperlinks) to be coded into hypernetworks. Such hypernetworks can distinguish between how pairwise interactions modulate a third agent (active HOI) and how the altered state of each agent in turn governs interactions between other agents (passive HOI). The simultaneous occurrence of active and passive HOI can drive complex systems to evolve at multiple time and space scales. We apply the model to reconstruct a hypernetwork of hexa-species microbial communities, and by dissecting the topological architecture of the hypernetwork using GLMY homology theory, we find distinct roles of pairwise interactions and HOI in shaping community behavior and dynamics. The statistical relevance of the hypernetwork model is validated using a series of in vitro mono-, co-, and tricultural experiments based on three bacterial species. [ABSTRACT FROM AUTHOR]

The non‐stoichiometry of material compounds significantly influences their functional properties. In semiconductors, point defects determine whether a material is n‐type or p‐type and the concentration of charge carriers. Even in structural alloys and ion conductors used in batteries and fuel cells, non‐stoichiometry and dilute defects play an integral role in their function. The design of metal alloys has advanced rapidly with the aid of thermodynamic modeling using calculation of phase diagrams (CALPHAD) to predict the phases produced during different processing conditions. While thermodynamic modeling has been done previously by fitting experimental data, the advent of first‐principle techniques has enabled the computational prediction of material properties. The defect energy formalism (DEF) is described for modeling charged and uncharged defects in compounds, showing that it accurately predicts non‐stoichiometry using density functional theory (DFT), without fitting experiments. The model reproduces the expected defect and free‐charge carrier concentrations using the statistical mechanics approach commonly used in most DFT defect studies. Finally, the model is used to accurately predict the single‐phase region of PbTe with no fitting to measured defect concentrations. This method can revolutionize materials development of insulators, semiconductors, and even metals by allowing rapid DFT calculations to replace laborious experiments when dilute defects are involved. [ABSTRACT FROM AUTHOR]

I argue that there are two distinct approaches to understanding reduction: the ontology-first approach and the theory-first approach. They concern the relation between ontological reduction and inter-theoretic reduction. Further, I argue for the significance of this distinction by demonstrating that either one or the other approach has been taken as an implicit assumption in, and has in fact shaped, our understanding of what statistical mechanics is. More specifically, I argue that Boltzmannian statistical mechanics assumes and relies on the ontology-first approach, whereas Gibbsian statistical mechanics should assume the theory-first approach. [ABSTRACT FROM AUTHOR]

Theoretical studies of the diffusional isotope effect in solids are still stuck in the 1960s and 1970s. With the development of high spatial resolution mass spectrometers, isotopic data of mineral grains are rapidly accumulated. To dig up information from these data, molecular-level theoretical models are urgently needed. Based on the microscopic definition of the diffusion coefficient (D), a new theoretical framework for calculating the diffusional isotope effect (DIE(v)) (in terms of D*/D) for vacancy-mediated impurity diffusion in solids is provided based on statistical mechanics formalism. The newly derived equation shows that the DIE(v) can be easily calculated as long as the vibration frequencies of isotope-substituted solids are obtained. The calculated DIE(v) values of 199Au/195Au and 60Co/57Co during diffusion in Cu and Au metals are all within 1% of errors compared to the experimental data, which shows that this theoretical model is reasonable and precise. [ABSTRACT FROM AUTHOR]

This paper introduces and explains cyber physics, which we define as mathematical equations, i.e., physics-like laws, that control, regulate, or otherwise govern the inner workings of the hardware architecture, operating system, application code, algorithms, and networks on a classical computing machine. Cyber physics integrates computer science with conventional physics, in particular with quantum physics, thermodynamics, and statistical mechanics. Naturally, the technical description of cyber physics in the paper draws on both of these fields of science. [ABSTRACT FROM AUTHOR]

AbstractBetween the two world wars, a group of Italian mathematicians, statisticians and economists set out to use the tools of statistical mechanics to interpret the Pareto income distribution curve as a probability distribution. Models based on Boltzmann's thermal equilibrium were independently developed to find an economic variable, comparable to the kinetic energy of gas theory, that could explain the heavy tail of the Pareto curve. The various avenues explored eventually led them back to Pareto's much debated explanation, namely that the hyperbolic distribution of income was due to the unequal distribution of talent. [ABSTRACT FROM AUTHOR]

In this paper, we aim to study the three-dimensional N = 2 supersymmetric dual gauge theories on S b 3 / Z r in the context of the gauge/YBE correspondence. We consider hyperbolic integral identities acquired via the equality of supersymmetric lens partition functions as solutions to the decoration transformation and the flipping relation in statistical mechanics. The solutions of those transformations aim at investigating various decorated lattice models possessing the Boltzmann weights of integrable Ising-like models obtained via the gauge/YBE correspondence. We also constructed The Bailey pairs for the decoration transformation and the flipping relation. [ABSTRACT FROM AUTHOR]

The claim that the free energy principle is somehow related to Hamilton's principle in statistical mechanics is ubiquitous throughout the subject literature. However, the exact nature of this relationship remains unclear. According to some sources, the free energy principle is merely similar to Hamilton's principle of stationary action; others claim that it is either analogous or equivalent to it, while yet another part of the literature espouses the claim that it is a version of Hamilton's principle. In this article, we aim to clarify the nature of the relationship between the two principles by investigating the two most likely interpretations of the claims that can be found in the subject literature. According to the strong interpretation, the two principles are equivalent and apply to the same subset of physical phenomena; according to the weak interpretation, the two principles are merely analogous to each other by virtue of their similar formal structures. As we show, adopting the stronger reading would lead to a dilemma that is untenable for the proponents of the free energy principle, thus supporting the adoption of the weaker reading for the relationship between the two constructs. [ABSTRACT FROM AUTHOR]

A mathematical model is established to investigate the economic effects of infectious diseases. The distribution of wealth among two types of agents in the context of the epidemic is discussed. Using the method of statistical mechanics, the evolution of the entropy weak solutions for the model of the susceptible and the infectious involving wealth density functions is analyzed. We assume that as time tends to infinity, the wealth density function of the infectious is linearly related to the wealth density function of the susceptible individuals. Our results indicate that the spreading of disease significantly affects the wealth distribution. When time tends to infinity, the total wealth density function behaves as an inverse gamma distribution. Utilizing numerical experiments, the distribution of wealth under the epidemic phenomenon and the situation of wealth inequality among agents are discussed. [ABSTRACT FROM AUTHOR]

After reviewing the peculiar thermodynamics and statistical mechanics of self-gravitating systems, we consider the case of a "binary star" consisting of two particles of size a in gravitational interaction in a box of radius R. The caloric curve of this system displays a region of negative specific heat in the microcanonical ensemble, which is replaced by a first-order phase transition in the canonical ensemble. The free energy viewed as a thermodynamic potential exhibits two local minima that correspond to two metastable states separated by an unstable maximum forming a barrier of potential. By introducing a Langevin equation to model the interaction of the particles with the thermal bath, we study the random transitions of the system between a "dilute" state, where the particles are well separated, and a "condensed" state, where the particles are bound together. We show that the evolution of the system is given by a Fokker–Planck equation in energy space and that the lifetime of a metastable state is given by the Kramers formula involving the barrier of free energy. This is a particular case of the theory developed in a previous paper (Chavanis, 2005) for N Brownian particles in gravitational interaction associated with the canonical ensemble. In the case of a binary star ( N = 2 ), all the quantities can be calculated exactly analytically. We compare these results with those obtained in the mean field limit N → + ∞ . [ABSTRACT FROM AUTHOR]

In this paper, we rigorously prove Boltzmann's entropy formula S = k log W in classical unbounded spin systems. By restricting our consideration to negatively interacting super-stable potentials, we prove the existence of pressure and the concavity of micro-canonical entropy corresponding to log W. Notably, the lattice φ ν 4 model becomes a feasible example through the exploitation of the physical equivalence of potentials. Our proof is mostly based on a cut-off technique for configuration spaces that enables us to lift-up the results for bounded systems. This approach is independent of the existence of Gibbs states and, moreover, holds a clear mathematical conciseness. [ABSTRACT FROM AUTHOR]

Interacting particle systems in a finite-volume in equilibrium are often described by a grand-canonical ensemble induced by the corresponding Hamiltonian, i.e. a finite-volume Gibbs measure. However, in practice, directly measuring this Hamiltonian is not possible, as such, methods need to be developed to calculate the Hamiltonian potentials from measurable data. In this work, we give an expansion of the chemical potential in terms of the correlation functions of such a system in the thermodynamic limit. This is a justification of a formal approach of Nettleton and Green from the 50’s, that can be seen as an inverse cluster expansion. [ABSTRACT FROM AUTHOR]

The generalized mean-field orthoplicial model is a mean-field model on a space of continuous spins on R n that are constrained to a scaled (n - 1) -dimensional ℓ 1 -sphere, equivalently a scaled (n - 1) -dimensional orthoplex, and interact through a general interaction function. The finite-volume Gibbs states of this model correspond to singular probability measures. In this paper, we use probabilistic methods to rigorously classify the infinite-volume Gibbs states of this model, and we show that they are convex combinations of product states. The predominant methods utilize the theory of large deviations, relative entropy, and equivalence of ensembles, and the key technical tools utilize exact integral representations of certain partition functions and locally uniform estimates of expectations of certain local observables. [ABSTRACT FROM AUTHOR]

Landauer's principle is, roughly, the principle that logically irreversible operations cannot be performed without dissipation of energy, with a specified lower bound on that dissipation. Although widely accepted in the literature on the thermodynamics of computation, it has been the subject of considerable dispute in the philosophical literature. Proofs of the principle have been questioned on the grounds of insufficient generality and on the grounds of the assumption, used in the proofs, of the availability of reversible processes at the microscale. The relevance of the principle, should it be true, has also been questioned, as it has been argued that microscale fluctuations entail dissipation that always greatly exceeds the Landauer bound. In this article Landauer's principle is treated within statistical mechanics, and a proof of the principle is given that neither relies on neglect of fluctuations nor assumes the availability of thermodynamically reversible processes. In addition, it is argued that microscale fluctuations are no obstacle to approximating thermodynamic reversibility, in the appropriate sense, as closely as one would like. [ABSTRACT FROM AUTHOR]

This article outlines a novel interpretation of quantum theory: the Q-based interpretation. The core idea underlying this interpretation, recently suggested for quantum field theories by Drummond and Reid, is to interpret the phase space function Q —a transform of the better known Wigner function—as a proper probability distribution, roughly analogous to the probability distribution ρ in classical statistical mechanics. Here I motivate the Q-based interpretation, investigate whether it is empirically adequate, and outline some of its key conceptual features. I argue that the Q-based interpretation is attractive in that it promises having no measurement problem, is conceptually parsimonious, and has the potential to apply elegantly to relativistic and field-theoretic contexts. [ABSTRACT FROM AUTHOR]

Copyright of Nonferrous Metals (Mineral Processing Section) is the property of Beijing Research Institute of Mining & Metallurgy Technology Group and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

This paper examines no-hidden-variables theorems in quantum mechanics from the point of view of statistical mechanics. It presents a general analysis of the measurement process in the Boltzmannian framework that leads to a characterization of (in)compatible measurements and reproduces several features of quantum probabilities often described as "non-classical". The analysis is applied to versions of the Kochen–Specker and Bell theorems to shed more light on their implications. It is shown how, once the measurement device and the active role of the measurement process are taken into account, contextuality appears as a natural feature of random variables. This corroborates Bell's criticism that no-go results of the Kochen–Specker type are based on gratuitous assumptions. In contrast, Bell-type theorems are much more profound, but should be understood as nonlocality theorems rather than no-hidden-variables theorems. Finally, the paper addresses misunderstandings and misleading terminology that have confused the debate about hidden variables in quantum mechanics. [ABSTRACT FROM AUTHOR]

This paper examines no-hidden-variables theorems in quantum mechanics from the point of view of statistical mechanics. It presents a general analysis of the measurement process in the Boltzmannian framework that leads to a characterization of (in)compatible measurements and reproduces several features of quantum probabilities often described as “non-classical”. The analysis is applied to versions of the Kochen–Specker and Bell theorems to shed more light on their implications. It is shown how, once the measurement device and the active role of the measurement process are taken into account, contextuality appears as a natural feature of random variables. This corroborates Bell’s criticism that no-go results of the Kochen–Specker type are based on gratuitous assumptions. In contrast, Bell-type theorems are much more profound, but should be understood as nonlocality theorems rather than no-hidden-variables theorems. Finally, the paper addresses misunderstandings and misleading terminology that have confused the debate about hidden variables in quantum mechanics.

Empirical force fields employed in molecular dynamics simulations of complex systems are often optimized to reproduce experimentally determined structural and thermodynamic properties. In contrast, experimental knowledge about the interconversion rates between metastable states in such systems is hardly ever incorporated in a force field due to a lack of an efficient approach. Here, we introduce such a framework based on the relationship between dynamical observables, such as rate constants, and the underlying molecular model parameters using the statistical mechanics of trajectories. Given a prior ensemble of molecular dynamics trajectories produced with imperfect force field parameters, the approach allows for the optimal adaption of these parameters such that the imposed constraint of equally predicted and experimental rate constant is obeyed. To do so, the method combines the continuum path ensemble maximum caliber approach with path reweighting methods for stochastic dynamics. When multiple solutions are found, the method selects automatically the combination that corresponds to the smallest perturbation of the entire path ensemble, as required by the maximum entropy principle. To show the validity of the approach, we illustrate the method on simple test systems undergoing rare event dynamics. Next to simple 2D potentials, we explore particle models representing molecular isomerization reactions and protein–ligand unbinding. Besides optimal interaction parameters, the methodology gives physical insights into what parts of the model are most sensitive to the kinetics. We discuss the generality and broad implications of the methodology. [ABSTRACT FROM AUTHOR]

The General Equation for Non-Equilibrium Reversible Irreversible Coupling (generic) framework provides a thermodynamically consistent approach to describe the evolution of coarse-grained variables. This framework states that Markovian dynamic equations governing the evolution of coarse-grained variables have a universal structure that ensures energy conservation (first law) and entropy increase (second law). However, the presence of external time-dependent forces can break the energy conservation law, requiring modifications to the framework's structure. To address this issue, we start from a rigorous and exact transport equation for the average of a set of coarse-grained variables derived from a projection operator technique in the presence of external forces. Under the Markovian approximation, this approach provides the statistical mechanics underpinning of the generic framework under external forcing conditions. By doing so, we can account for the effects of external forcing on the system's evolution while ensuring thermodynamic consistency. [ABSTRACT FROM AUTHOR]

Mitochondria serve a wide range of functions within cells, most notably via their production of ATP. Although their morphology is commonly described as bean-like, mitochondria often form interconnected networks within cells that exhibit dynamic restructuring through a variety of physical changes. Further, though relationships between form and function in biology are well established, the extant toolkit for understanding mitochondrial morphology is limited. Here, we emphasize new and established methods for quantitatively describing mitochondrial networks, ranging from unweighted graph-theoretic representations to multi-scale approaches from applied topology, in particular persistent homology. We also show fundamental relationships between mitochondrial networks, mathematics, and physics, using ideas of graph planarity and statistical mechanics to better understand the full possible morphological space of mitochondrial network structures. Lastly, we provide suggestions for how examination of mitochondrial network form through the language of mathematics can inform biological understanding, and vice versa.

Abstract We study the dynamical assembly of weighted bipartite networks to understand the hidden mechanisms of pollination, expanding the Bianconi–Barabási model where nodes have intrinsic properties. Allowing for a non-linear interaction rate, which represents the seasonality of flowers and pollinators, our analysis reveals similarity of this extended Bianconi–Barabási model with field observations. While our current approach may not fully account for the diverse range of interaction accretion slopes observed in the real world, we regard it as an important step towards enriching theoretical models with biological realism.

We attempt to construct a (two-dimensional) statistical mechanics description of the scenario in which the experiment in [T. Westphal et al., Nature 591, 225 (2021)] was made. It includes two masses that, simultaneously, (1) interact classically via the Newton gravitation and (2) harmonically vibrate. Within the strictures of Gibbs canonical ensemble at the temperature T, our treatment is exact. [ABSTRACT FROM AUTHOR]

We prove that the lowest free energy of a classical interacting system at temperature T with a prescribed density profile ρ(x) can be approximated by the local free energy ∫fT(ρ(x))dx, provided that ρ varies slowly over sufficiently large length scales. A quantitative error on the difference is provided in terms of the gradient of the density. Here fT is the free energy per unit volume of an infinite homogeneous gas of the corresponding uniform density. The proof uses quantitative Ruelle bounds (estimates on the local number of particles in a large system), which are derived in an appendix. [ABSTRACT FROM AUTHOR]

Urbanization and climate change are contributing to severe flooding globally, damaging infrastructure, disrupting economies, and undermining human well-being. Approaches to make cities more resilient to floods are emerging, notably with the design of flood-resilient structures, but relatively little is known about the role of urban form and its complexity in the concentration of flooding. We leverage statistical mechanics to reduce the complexity of urban flooding and develop a mean-flow theory that relates flood hazards to urban form characterized by the ground slope, urban porosity, and the Mermin order parameter which measures symmetry in building arrangements. The mean-flow theory presents a dimensionless flood depth that scales linearly with the urban porosity and the order parameter, with different scaling for disordered square- and hexagon-like forms. A universal scaling is obtained by introducing an effective mean chord length representative of the unobstructed downslope travel distance for flood water, yielding an analytical model for neighborhood-scale flood hazards globally. The proposed mean-flow theory is applied to probe city-to-city variations in flood hazards, and shows promising results linking recorded flood losses to urban form and observed rainfall extremes. A statistical mechanics approach unveils how urban layout influences flood hazards linking flood risk to factors like ground slope, porosity, building arrangement symmetry, and chord length, offering a scalable model applicable worldwide. [ABSTRACT FROM AUTHOR]

We consider a class of nonequilibrium systems of interacting agents with pairwise interactions and quenched disorder in the dynamics featuring, in the thermodynamic limit, phase transitions. We identify mathematical conditions on the microscopic interaction structure, namely the separability of the interaction kernel, that lead to a dimension reduction of the system in terms of a finite number of reaction coordinates (RCs). Such RCs prove to be proper nonequilibrium thermodynamic variables as they carry information on correlation, memory and resilience properties of the system. Phase transitions can be identified and quantitatively characterised as singularities of the complex valued susceptibility functions associated to the RCs. We provide analytical and numerical evidence of how the singularities affect the physical properties of finite size systems. [ABSTRACT FROM AUTHOR]

Stratified rock masses comprise various rocks with different thicknesses, lithologies, and compositions. They exhibit unique cracking morphology and failure modes when subjected to external loads. Understanding and mastering the fracture morphology and failure laws of stratified rock masses under three-dimensional mechanical conditions is crucial for researching disasters in underground engineering geology. This paper presents a three-dimensional double-layer rock mass model established using the numerical calculation method based on mesoscopic statistical damage mechanics. The model simulates the cracking mode of the rock surface under biaxial tensile conditions. The simulation results are quantified using PCAS software. Crack indexes, such as the number of cracked blocks, average cracked block area, and surface crack rate, are used to evaluate the degree of influence of different factors on the cracking of the rock surface layer. The results indicate that the degree of surface crack development varies linearly with the degree of homogeneity (m). Additionally, the layer thickness ratio (η) is positively correlated with the average fragmentation area, and the two are logarithmic. Regardless of the model scale, the average circumference of each block is approximately equal to the model side length. The model exhibits the highest degree of crack development when the loads in the x and y directions are equal. Moreover, the degree of crack development in the model is also influenced by the loading per step, and the two are proportional. [ABSTRACT FROM AUTHOR]

A theoretical approach aimed at the quantum statistical mechanics of a molecular ensemble coupled to a lossless cavity mode is presented. A canonical ensemble is considered and an approximate formula is devised for the Helmholtz free energy correction due to cavity-molecule coupling, which enables the derivation of experimentally measurable thermodynamic quantities. The frequency of the cavity mode is assumed to lie in the infrared range. Therefore, the cavity couples to molecular vibrations and our treatment is restricted to the electronic ground state of the molecule. The method is tested for an analytically solvable model system of one-dimensional harmonic oscillators coupled to the cavity. The performance of the approximation and its range of validity are discussed in detail. It is shown that the leading-order correction to the Helmholtz free energy is proportional to the square of the collective coupling strength. We also demonstrate that the cavity mode does not have a significant impact on the thermodynamic properties of the system in the collective ultrastrong coupling regime (the collective coupling strength is comparable to the frequency of the cavity mode). [ABSTRACT FROM AUTHOR]

After the completion of in situ pyrolysis, oil shale can be used as a natural place for CO2 sequestration. However, the effects of chemical action and formation stress-state changes on the deformation of oil shale should be considered when CO2 is injected into oil shale after pyrolysis. In this study, combined with statistical damage mechanics, a transverse isotropic model of oil shale with coupled damage mechanisms was established by considering the decreased mechanical properties and the chemical damage caused by CO2 injection. The process of injecting supercritical CO2 into oil shale after pyrolysis was simulated by COMSOL6.0. The volume distribution of CO2 and the stress evolution in oil shale were analyzed. It is found that CO2 injection into oil shale after pyrolysis will not produce new force damage, and the force damage caused by the decrease in the mechanical properties of oil shale after pyrolysis can offset the ground uplift caused by CO2 injection to a certain extent. Under the combined action of chemical damage and mechanical damage, the uplift of a formation with a thickness of 200 m is only 10 cm. The injection of supercritical CO2 is beneficial for maintaining the stability of oil shale after in situ pyrolysis. [ABSTRACT FROM AUTHOR]

In this paper, the pathway model for the real scalar variable case is re-explored and its connections to fractional integrals, solutions of fractional differential equations, Tsallis statistics and superstatistics in statistical mechanics, the reaction-rate probability integral, Krätzel transform, pathway transform, etc., are explored. It is shown that the common thread in these connections is their H-function representations. The pathway parameter is shown to be connected to the fractional order in fractional integrals and fractional differential equations. [ABSTRACT FROM AUTHOR]

In this research article, we demonstrate the generalized expansion method to investigate nonlinear integro-partial differential equations via an efficient mathematical method for generating abundant exact solutions for two types of applicable nonlinear models. Moreover, stability analysis and modulation instability are also studied for two types of nonlinear models in this present investigation. These analyses have several applications including analyzing control systems, engineering, biomedical engineering, neural networks, optical fiber communications, signal processing, nonlinear imaging techniques, oceanography, and astrophysical phenomena. To study nonlinear PDEs analytically, exact traveling wave solutions are in high demand. In this paper, the (1 + 1)-dimensional integro-differential Ito equation (IDIE), relevant in various branches of physics, statistical mechanics, condensed matter physics, quantum field theory, the dynamics of complex systems, etc., and also the (2 + 1)-dimensional integro-differential Sawda–Kotera equation (IDSKE), providing insights into the several physical fields, especially quantum gravity field theory, conformal field theory, neural networks, signal processing, control systems, etc., are investigated to obtain a variety of wave solutions in modern physics by using the mentioned method. Since abundant exact wave solutions give us vast information about the physical phenomena of the mentioned models, our analysis aims to determine various types of traveling wave solutions via a different integrable ordinary differential equation. Furthermore, the characteristics of the obtained new exact solutions have been illustrated by some figures. The method used here is candid, convenient, proficient, and overwhelming compared to other existing computational techniques in solving other current world physical problems. This article provides an exemplary practice of finding new types of analytical equations. [ABSTRACT FROM AUTHOR]

The generalization of the virial theorem, introduced by Clausius in statistical mechanics, has recently been carried out in the framework of geometric approaches to Hamiltonian and Lagrangian theories and it has been formulated in an intrinsic way. It is here revisited not only in its more general situation of a generic vector field but mainly from the perspective of contact and cosymplectic geometry. The previous generalizations allowing virial like relations from one-parameter groups of non-strictly canonical transformations and the rôle of Killing and conformal Killing vector fields for Lagrangians of a mechanical type are here completed with the theory for contact Hamiltonian, as well as gradient and evolution, vector fields. The corresponding theories in the framework of cosymplectic geometry and the particular case of time-dependent vector fields are also developed. [ABSTRACT FROM AUTHOR]

The existence of multiple biomolecular condensates inside living cells is a peculiar phenomenon not compatible with the predictions of equilibrium statistical mechanics. In this work, we address the problem of multiple condensates state (MCS) from a functional perspective. We combine Langevin dynamics, reaction-diffusion simulation, and dynamical systems theory to demonstrate that MCS can indeed be a function optimization strategy. Using Arp2/3 mediated actin nucleation pathway as an example, we show that actin polymerization is maximum at an optimal number of condensates. For a fixed amount of Arp2/3, MCS produces a greater response compared to its single condensate counterpart. Our analysis reveals the functional significance of the condensate size distribution which can be mapped to the recent experimental findings. Given the spatial heterogeneity within condensates and non-linear nature of intracellular networks, we envision MCS to be a generic functional solution, so that structures of network motifs may have evolved to accommodate such configurations. Biomolecular condensates often appear as a multi-droplet system inside living cells. Here, using multi-scale simulations, the authors show that such configurations are functionally more efficient in catalyzing cell signaling. [ABSTRACT FROM AUTHOR]

The current experimental capabilities do not allow researchers to measure the surface tension of aluminum without an oxide layer on its surface. Therefore, the oxide-free, or intrinsic, surface tension must still be estimated from first principles. For this purpose, the original model proposed by Skapski for estimating surface tension, and its subsequent modifications have been analyzed in this study. In addition, significant structures and statistical mechanics models have also been evaluated. Moreover, a new Skapski modification has been developed, with the enthalpy of vaporization term changing with temperature. Based on the comparison of these models with maximum experimental results from the literature, as well as analysis of the temperature coefficients, it is suggested that the intrinsic surface tension of liquid aluminum be estimated by the new modification. [ABSTRACT FROM AUTHOR]

Transcription has a mechanical component, as the translocation of the transcription machinery or RNA polymerase (RNAP) on DNA or chromatin is dynamically coupled to the chromatin torsion. This posits chromatin mechanics as a possible regulator of eukaryotic transcription, however, the modes and mechanisms of this regulation are elusive. Here, we first take a statistical mechanics approach to model the torsional response of topology-constrained chromatin. Our model recapitulates the experimentally observed weaker torsional stiffness of chromatin compared to bare DNA and proposes structural transitions of nucleosomes into chirally distinct states as the driver of the contrasting torsional mechanics. Coupling chromatin mechanics with RNAP translocation in stochastic simulations, we reveal a complex interplay of DNA supercoiling and nucleosome dynamics in governing RNAP velocity. Nucleosomes play a dual role in controlling the transcription dynamics. The steric barrier aspect of nucleosomes in the gene body counteracts transcription via hindering RNAP motion, whereas the chiral transitions facilitate RNAP motion via driving a low restoring torque upon twisting the DNA. While nucleosomes with low dissociation rates are typically transcriptionally repressive, highly dynamic nucleosomes offer less of a steric barrier and enhance the transcription elongation dynamics of weakly transcribed genes via buffering DNA twist. We use the model to predict transcription-dependent levels of DNA supercoiling in segments of the budding yeast genome that are in accord with available experimental data. The model unveils a paradigm of DNA supercoilingmediated interaction between genes and makes testable predictions that will guide experimental design. [ABSTRACT FROM AUTHOR]

In spring 1949 about 70 physicists from eight countries met in Florence to discuss recent trends in statistical mechanics. This scientific gathering, co-organized by the Commission on Thermodynamics and Statistical Mechanics of the International Union of Pure and Applied Physics (IUPAP) and the Italian Physical Society (SIF), initiated a tradition of IUPAP-sponsored international conferences on statistical mechanics that lasts to this day. In 1977, when this conference series took the name of StatPhys, the foundational role of the Florence conference was recognized by retrospectively naming it StatPhys1. This paper examines the dual scientific and social significance of the conference, situating it in the broader contexts of the post-World War II reconstruction in Italian physics and of the revitalization of the international science organization. Through an analysis of IUPAP archives and Italian records, we illustrate how the event's success hinged on the aligned objectives of its organizers. Internationally, it was instrumental in defining the scientific and organizational foundations for the activities of IUPAP commissions during a critical phase of IUPAP's history, when the Union was resurging on the international scene after the inactivity of the interwar period. Nationally, the conference served as a cornerstone in SIF's strategy to re-establish Italian physics' international stature and to aid the domestic revitalization of physics through the internationalization of its activities, notably of its flagship journal, Il Nuovo Cimento. This analysis not only sheds light on the conference's impact but also informs recent discussions in the history of science about the multiple roles of international scientific conferences. [ABSTRACT FROM AUTHOR]