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We analyze the general relation between canonical and grand canonical ensembles in the thermodynamic limit. We begin our discussion by deriving, with an alternative approach, some standard results first obtained by Kac and coworkers in the late 1970s. Then, motivated by the Bose–Einstein condensation (BEC) of trapped gases with a fixed number of atoms, which is well described by the canonical ensemble and by the recent groundbreaking experimental realization of BEC with photons in a dye-filled optical microcavity under genuine grand canonical conditions, we apply our formalism to a system of non-interacting Bose particles confined in a two-dimensional harmonic trap. We discuss in detail the mathematical origin of the inequivalence of ensembles observed in the condensed phase, giving place to the so-called grand canonical catastrophe of density fluctuations. We also provide explicit analytical expressions for the internal energy and specific heat and compare them with available experimental data. For these quantities, we show the equivalence of ensembles in the thermodynamic limit. [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]

Non-standard thermostatistical formalisms derived from generalizations of the Boltzmann–Gibbs entropy have attracted considerable attention recently. Among the various proposals, the one that has been most intensively studied, and most successfully applied to concrete problems in physics and other areas, is the one associated with the S q non-additive entropies. The S q -based thermostatistics exhibits a number of peculiar features that distinguish it from other generalizations of the Boltzmann–Gibbs theory. In particular, there is a close connection between the S q -canonical distributions and the micro-canonical ensemble. The connection, first pointed out in 1994, has been subsequently explored by several researchers, who elaborated this facet of the S q -thermo-statistics in a number of interesting directions. In the present work, we provide a brief review of some highlights within this line of inquiry, focusing on micro-canonical scenarios leading to S q -canonical distributions. We consider works on the micro-canonical ensemble, including historical ones, where the S q -canonical distributions, although present, were not identified as such, and also more resent works by researchers who explicitly investigated the S q -micro-canonical connection. [ABSTRACT FROM AUTHOR]

On the capital market, price movements of stock corporations can be observed independent of overall market developments as a result of company-specific news, which suggests the occurrence of a sudden risk event. In recent years, numerous concepts from statistical physics have been transferred to econometrics to model these effects and other issues, e.g., in socioeconomics. Like other studies, we extend the approaches based on the "buy" and "sell" positions of agents (investors' stance) with a third "hold" position. We develop the corresponding theory within the framework of the microcanonical and canonical ensembles for an ideal agent system and apply it to a capital market example. We thereby design a procedure to estimate the required model parameters from time series on the capital market. The aim is the appropriate modeling and the one-step-ahead assessment of the effect of a sudden risk event. From a one-step-ahead performance comparison with selected benchmark approaches, we infer that the model is well-specified and the model parameters are well determined. [ABSTRACT FROM AUTHOR]

We investigate the microstructural evolution of electrochemically deposited poly-crystalline Cu films during subsequent thermal process cycles at mild maximum temperatures, compatible with the integration in advanced metallization schemes for electronic device manufacturing. The modifications induced by the thermal budget have been characterized at different scales (from the film-substrate interface to the wafer scale) with different complementary techniques: X-ray Diffraction (XRD), scanning electron microscopy (SEM), atomic force microscopy (AFM), and dynamical warpage measurements. Moreover, the film internal grains' evolution has been modelled by a tri-dimensional on-cell model, derived by the Pott-like multi-states configurational energy dependence, able to consider multiple orientation of the grains and densification kinetics in the canonical ensemble. Finally, a macroscopic model of the warpage dependence on the process conditions is discussed. The presented joint theoretical and experimental analysis provides a complete and consistent scenario of the grain densification phenomenon and its impact for the Cu film microstructure and the composite system morphology, indicating several strategies for the integration of the process in real device structures. [ABSTRACT FROM AUTHOR]

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]

Although partition temperature derived using the Darwin–Fowler method is exact for simple scenarios, the derivation for complex systems might reside in specific approximations whose viability is not ensured if the thermodynamic limit is not attained. This work elaborates on a related problem relevant to relativistic high-energy collisions. On the one hand, it is simple enough that closed-form expressions can be obtained precisely for the one-particle distribution function. On the other hand, the resulting expression is not an exponential form, and therefore, it is not straightforward that the notion of partition function could be implied. Specifically, we derive the one-particle distribution function for massless particles where the phase-space integration is performed exactly for the underlying canonical ensemble consisting of a given number of particles. We discuss the viability of the partition temperature in this case. Possible implications of the obtained results regarding the observed Tsallis distribution in transverse momentum spectra in high-energy collisions are also addressed. [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]

A simple harmonic oscillator canonical ensemble model for Schwarzchild black hole quantum tunneling radiation is proposed in this paper. Firstly, the equivalence between canonical ensemble model and Parikh-Wilczek-s tunneling method is introduced. Then, radiated massless particles are considered as a collection of simple harmonic oscillators. Based on this model, we treat the black hole as a heat bath to derive the energy flux of the radiation. Finally, we apply the result to estimate the lifespan of a black hole. [ABSTRACT FROM AUTHOR]

It is common lore that the canonical gravitational partition function Z associated with the classical Boltzmann-Gibbs (BG) exponential distribution cannot be built up because of mathematical pitfalls. The integral needed for writing up Z diverges. We review here how to avoid this pitfall and obtain a (classical) statistical mechanics of Newton's gravitation. This is done using (1) the analytical extension treatment obtained of Gradshteyn and Rizhik and (2) the well known dimensional regularization technique.

This work scrutinizes, using statistical mechanics indicators, important traits displayed by quantum many-body systems. Our statistical mechanics quantifiers are employed, in the context of Gibbs' canonical ensemble at temperature T. A new quantifier of this sort is also presented here. The present discussion focuses attention on the role played by the fermion number N in many-fermion dynamics, that is, N is our protagonist. We have discovered discovers particular values of N for which the thermal indicators exhibit unexpected abrupt variations. Such a fact reflects an unanticipated characteristic of fermionic dynamics. [ABSTRACT FROM AUTHOR]

Maximum entropy network ensembles have been very successful in modelling sparse network topologies and in solving challenging inference problems. However the sparse maximum entropy network models proposed so far have fixed number of nodes and are typically not exchangeable. Here we consider hierarchical models for exchangeable networks in the sparse limit, i.e., with the total number of links scaling linearly with the total number of nodes. The approach is grand canonical, i.e., the number of nodes of the network is not fixed a priori: it is finite but can be arbitrarily large. In this way the grand canonical network ensembles circumvent the difficulties in treating infinite sparse exchangeable networks which according to the Aldous-Hoover theorem must vanish. The approach can treat networks with given degree distribution or networks with given distribution of latent variables. When only a subgraph induced by a subset of nodes is known, this model allows a Bayesian estimation of the network size and the degree sequence (or the sequence of latent variables) of the entire network which can be used for network reconstruction. [ABSTRACT FROM AUTHOR]

We assess the degree of quantumness of the P, Q, and W quantum optics' approximations in a thermal context governed by the canonical ensemble treatment. First, we remint the reader of the bridge connecting quantum optics with statistical mechanics using the abovementioned approximations at the temperature T. With the ensuing materials, we explore with some detail some features of the above bridge, related to the entropy and to thermal uncertainties. Some new relations concerning the degree of quantumness of the P, Q, and W are obtained by comparison between them and the exact and classical treatments. [ABSTRACT FROM AUTHOR]

Canonical ensembles of walks in a finite connected graph assign the properly normalized probability distributions to all nodes, subgraphs, and nodal subsets of the graph at all time and connectivity scales of the diffusion process. The probabilistic description of graphs allows for introducing the quantitative measures of navigability through the graph, walkability of individual paths, and mutual perspicacity of the different modes of the (diffusion) processes. The application of information theory methods to problems about graphs, in contrast to geometric, combinatoric, algorithmic, and algebraic approaches, can be called information graph theory. As it involves evaluating communication efficiency between individual systems' units at different time and connectivity scales, information graph theory is in demand for a wide range of applications, such as designing network-on-chip architecture and engineering urban morphology within the concept of the smart city. [ABSTRACT FROM AUTHOR]

We provide a detailed description of the path-integral Monte Carlo worm algorithm used to exactly calculate the thermodynamics of Bose systems in the canonical ensemble. The algorithm is fully consistent with periodic boundary conditions, which are applied to simulate homogeneous phases of bulk systems, and it does not require any limitation in the length of the Monte Carlo moves realizing the sampling of the probability distribution function in the space of path configurations. The result is achieved by adopting a representation of the path coordinates where only the initial point of each path is inside the simulation box, the remaining ones being free to span the entire space. Detailed balance can thereby be ensured for any update of the path configurations without the ambiguity of the selection of the periodic image of the particles involved. We benchmark the algorithm using the non-interacting Bose gas model for which exact results for the partition function at finite number of particles can be derived. Convergence issues and the approach to the thermodynamic limit are also addressed for interacting systems of hard spheres in the regime of high density. [ABSTRACT FROM AUTHOR]

The notion of statistical order derives from the disequilibrium concept introduced by López-Ruiz, Mancini, and Calbet thirty years ago. In this effort, it is shown that the disequilibrium is intimately linked to the celebrated Rényi entropy. One also explores this link in connection with the van der Waals gas description. [ABSTRACT FROM AUTHOR]

The Wigner-Kirkwood expansion of the quantum correction to the classical free energy is generally said to be in powers of ℏ 2 and only its first few terms are presented. In this work, we use the Bloch differential equation to obtain a general description of all terms in a dimensionless form. The first corrective term turns out to be proportional to the product of λ 2 / a 2 , where λ is the thermal de Broglie wavelength and a 3 is the volume per particle, by an effective coupling constant. This dimensionless parameter can be used to assess the magnitude of the quantum correction. Using the one-component plasma as an illustration we highlight the importance of the magnitude of the potential on the quantum correction. The results presented are not formally new; the emphasis is placed on a simple and didactic presentation. [ABSTRACT FROM AUTHOR]

Sodium chloride (NaCl) represents the principal component of atmospheric particulates of marine origin. To gain a molecular-level understanding of the adsorption process of water vapor on the NaCl surface, Monte Carlo simulations performed in the Grand Canonical ensemble were carried out, considering the water adsorption at different water pressures on a NaCl(001) surface. The calculated adsorption isotherm shows four different regions, whose coverages correspond to those of the low-, transition-, high-, and pre-solution-coverage regions experimentally observed. Detailed analysis reveals how the structure of the adsorbed water molecules (islands, layer, and multi-layer) changes depending on water pressure, and how their orientation with respect to the surface varies with the distance from the surface. This detailed information further supports the picture coming from previous experimental IR absorption spectroscopy studies. [ABSTRACT FROM AUTHOR]

This paper seeks to advance the state-of-the-art in analysing fMRI data to detect onset of Alzheimer's disease and identify stages in the disease progression. We employ methods of network neuroscience to represent correlation across fMRI data arrays, and introduce novel techniques for network construction and analysis. In network construction, we vary thresholds in establishing BOLD time series correlation between nodes, yielding variations in topological and other network characteristics. For network analysis, we employ methods developed for modelling statistical ensembles of virtual particles in thermal systems. The microcanonical ensemble and the canonical ensemble are analogous to two different fMRI network representations. In the former case, there is zero variance in the number of edges in each network, while in the latter case the set of networks have a variance in the number of edges. Ensemble methods describe the macroscopic properties of a network by considering the underlying microscopic characterisations which are in turn closely related to the degree configuration and network entropy. When applied to fMRI data in populations of Alzheimer's patients and controls, our methods demonstrated levels of sensitivity adequate for clinical purposes in both identifying brain regions undergoing pathological changes and in revealing the dynamics of such changes. [ABSTRACT FROM AUTHOR]

Steady-state two-phase flow in porous media is a process whereby a wetting phase displaces a non-wetting phase within a pore network. It is an off-equilibrium stationary process--in the sense that it is maintained in dynamic equilibrium at the expense of energy supplied to the system. The efficiency of the process depends on its spontaneity, measurable by the rate of global entropy production. The latter has been proposed to comprise two components: the rate of mechanical energy dissipation at constant temperature (a thermal entropy component, Q/T, in the continuum mechanics scale) and the configurational entropy (a Boltzmann-Gibbs entropy component, klnW), due to the existence of a canonical ensemble of flow configurations, physically admissible to the externally imposed macrostate conditions. Here, we propose an analytical model to account the number of microstates, lnW, in two-phase flows in pore networks. Combinatorial analysis is implemented to evaluate the number of identified microstates per physically admissible internal flow arrangement, compatible with the imposed steady-state flow conditions. Then, Stirling's approximation is applied to downscale the large factorial numbers. Finally, the number of microstates is estimated by contriving an appropriate mixing scheme over the canonical ensemble of the physically admissible flow configurations. Indicative computations are furnished. [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]

We calculated the magnetocaloric properties of the molecular nanomagnet Cu5-NIPA, consisting of five spins S = 1 / 2 arranged in two corner-sharing triangles (hourglass-like structure without magnetic frustration). The thermodynamics of the system in question was described using the quantum Heisenberg model solved within the field ensemble (canonical ensemble) using exact numerical diagonalization. The dependence of the magnetic entropy and magnetic specific heat on the temperature and the external magnetic field was investigated. The isothermal entropy change for a wide range of initial and final magnetic fields was discussed. Due to plateau-like behavior of the isothermal entropy change as a function of the temperature, a high degree of tunability of magnetocaloric effect with the initial and final magnetic field was demonstrated. [ABSTRACT FROM AUTHOR]

Ms. Hui Wu and Professor Edwin R. Hancock should be added to the list of contributing authors. The updated "Author Contributions" is provided below: Author Contributions J.W. contributed to the formal analysis, investigation, methodology, and writing of the original manuscript. The previous authorship was Jianjia Wang, Xichen Wu, Mingrui Li, and the updated authorship is Jianjia Wang, Xichen Wu, Mingrui Li, Hui Wu, Edwin R. Hancock. [Extracted from the article]

In this paper, we present the supervised multi-view canonical correlation analysis ensemble (SMVCCAE) and its semi-supervised version (SSMVCCAE), which are novel techniques designed to address heterogeneous domain adaptation problems, i.e., situations in which the data to be processed and recognized are collected from different heterogeneous domains. Specifically, the multi-view canonical correlation analysis scheme is utilized to extract multiple correlation subspaces that are useful for joint representations for data association across domains. This scheme makes homogeneous domain adaption algorithms suitable for heterogeneous domain adaptation problems. Additionally, inspired by fusion methods such as Ensemble Learning (EL), this work proposes a weighted voting scheme based on canonical correlation coefficients to combine classification results in multiple correlation subspaces. Finally, the semi-supervised MVCCAE extends the original procedure by incorporating multiple speed-up spectral regression kernel discriminant analysis (SRKDA). To validate the performances of the proposed supervised procedure, a single-view canonical analysis (SVCCA) with the same base classifier (Random Forests) is used. Similarly, to evaluate the performance of the semi-supervised approach, a comparison is made with other techniques such as Logistic label propagation (LLP) and the Laplacian support vector machine (LapSVM). All of the approaches are tested on two real hyperspectral images, which are considered the target domain, with a classifier trained from synthetic low-dimensional multispectral images, which are considered the original source domain. The experimental results confirm that multi-view canonical correlation can overcome the limitations of SVCCA. Both of the proposed procedures outperform the ones used in the comparison with respect to not only the classification accuracy but also the computational efficiency. Moreover, this research shows that canonical correlation weighted voting (CCWV) is a valid option with respect to other ensemble schemes and that because of their ability to balance diversity and accuracy, canonical views extracted using partially joint random view generation are more effective than those obtained by exploiting disjoint random view generation. [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]

Understanding of the defect evolution mechanism under irradiation is very important for the research of pressure vessel steel embrittlement. In this paper, the embedded atom method (EAM) based canonical ensemble molecular dynamics (MD) method was used to study the evolution of the stacking structure of different nano-sized Cun (n = 13, 43 and 87) clusters in an Febulk embedded with BCC lattice structure during continuous heating. The mean square displacement, pair distribution functions and atomic structures of Cu atom clusters at the nanometer scale were calculated at different temperatures. The structural changes present apparent differences, for the Febulks contain nano-sized Cu clusters with different atom numbers during heating. For the Febulk–Cu13 system, since the ability to accommodate the atomic Cu in the Fe substrate is lesser, a small number of Cu atoms in BCC lattice positions cannot influence the whole structure of the Fe-Cu system. For the Febulk–Cu43 system, with an increase in temperature, a Cu atomic pile structural change happened, and the strain areas decreased significantly in the Febulk, but a single strain area grew large. For the Febulk–Cu87 system, when the Cu atoms are constrained by the Fe atoms in bulk, only a few of the Cu atoms adjust their positions. With the increase in temperature, strain in the Fe eased. [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 paper presents a computational study of the magnetocaloric properties of the V12 polyoxovanadate molecular magnet. The description is restricted to low-temperature range (below approximately 100 K), where the magnetic properties of the system in question can be sufficiently modelled by considering a tetramer that consists of four vanadium ions with spins S = 1 / 2 . The discussion is focused on the magnetocaloric effect in the cryogenic range. The exact and numerical diagonalization of the corresponding Hamiltonian is used in order to construct the thermodynamic description within a version of the canonical ensemble. The thermodynamic quantities of interest, such as magnetic entropy, specific heat, entropy change under isothermal magnetization/demagnetization, temperature change under adiabatic magnetization/demagnetization, refrigerant capacity, and magnetic Grüneisen ratio, are calculated and discussed extensively. The importance of two quantum level crossings for the described properties is emphasized. The significant ranges of direct and inverse magnetocaloric effect are predicted. In particular, the maximized inverse magnetocaloric response is found for cryogenic temperatures. [ABSTRACT FROM AUTHOR]

Our subject of interest here is entropic forces, as re-interpreted by Verlinde with reference to gravitation, that is, by appealing to Verlinde's conception of an entropic (statistically emergent) gravity advanced in [Physica A 2018, 511, 139]. In a canonical ensemble framework, we will deal with a non relativistic quantum scenario. In it, we perform a non-relativistic Schrödinger treatment (ST) of gravity as an entropic force and are able to detect new kinds of bounded quantum gravitational states, not previously reported. These new bound states would provide us with a novel energy-source, not taken into account as yet. The present entropic force deviates from the Newton's form only at extremely short distances. We propose, by specializing our results to gravitationally interacting bosons, a model for dark matter generation. [ABSTRACT FROM AUTHOR]

Purifying biogas can enhance the performance of distributed smart grid systems while potentially yielding clean feedstock for downstream usage such as steam reforming. Recently, a novel anion-pillared metal–organic framework (MOF) was reported in the literature that shows good capacity to separate acetylene from carbon dioxide. The present study assesses the usefulness of this adsorbent for separating a typical biogas mixture (consisting of methane, nitrogen, oxygen, hydrogen, carbon dioxide, and hydrogen sulphide) using a multiscale approach. This approach couples atomistic Monte Carlo simulations in the grand canonical ensemble with the batch equilibrium modelling of a pressure swing adsorption system. The metal–organic framework displays selectivity at low pressures for carbon dioxide and especially hydrogen sulphide. An analysis of adsorption isotherm models coupled with statistical distributions of surface–gas interaction energies determined that both CH4 and CO2 exhibited Langmuir-type adsorption, while H2S displayed Langmuir-type behaviour at low pressures, with increasing adsorption site heterogeneity at high pressures. Batch equilibrium modelling of a vacuum swing adsorption system to purify a CH4/CO2 feedstock demonstrated that such a system can be incorporated into a solar biogas reforming process since the target purity of 93–94 mol-% methane for incorporation into the process was readily achievable. [ABSTRACT FROM AUTHOR]

Surface charges of catalysts have important influences on the thermodynamics and kinetics of electrochemical reactions. Herein, we develop a modified version of the grand-canonical potential kinetics (GCP-K) method based on density functional theory (DFT) calculations to explore the effect of surface charges on reaction thermodynamics and kinetics. Using the hydrogen evolution reaction (HER) on the Pt(111) surface as an example, we show how to track the change of surface charge in a reaction and how to analyze its influence on the kinetics. Grand-canonical calculations demonstrate that the optimum hydrogen adsorption energy on Pt under the standard hydrogen electrode condition (SHE) is around −0.2 eV, rather than 0 eV established under the canonical ensemble, due to the high density of surface negative charges. By separating the surface charges that can freely exchange with the external electron reservoir, we obtain a Tafel barrier that is in good agreement with the experimental result. During the Tafel reaction, the net electron inflow into the catalyst leads to a stabilization of canonical energy and a destabilization of the charge-dependent grand-canonical component. This study provides a practical method for obtaining accurate grand-canonical reaction energetics and analyzing the surface charge induced changes. [ABSTRACT FROM AUTHOR]

A theoretical model was selected among three potentially applicable models and then used to analyze the absorption isotherms of the hydrogen storage alloys LaNi5 and LaNi4.75Pb0.25 at three different temperatures (T = 303 K, 313 K, 323 K). The theoretical expressions of the model were based on the statistical physics formalism and simplifying hypotheses. The model selected was the one with the highest correlation with the experimental data. The model had six adjustable parameters: the number of hydrogen atoms per site n α , n β , the receptor site densities N α , N β and the energy parameters P α , P β . The fitted parameters obtained for the Pb-doped and nondoped alloys were compared and discussed in relationship to the absorption isotherms. Finally, the fitted parameters or the model were further applied to calculate thermodynamic functions, such as entropy, Gibbs free energy and internal energy, which govern the absorption mechanism. [ABSTRACT FROM AUTHOR]

The micro-canonical, canonical, and grand canonical ensembles of walks defined in finite connected undirected graphs are considered in the thermodynamic limit of infinite walk length. As infinitely long paths are extremely sensitive to structural irregularities and defects, their properties are used to describe the degree of structural imbalance, anisotropy, and navigability in finite graphs. For the first time, we introduce entropic force and pressure describing the effect of graph defects on mobility patterns associated with the very long walks in finite graphs; navigation in graphs and navigability to the nodes by the different types of ergodic walks; as well as node's fugacity in the course of prospective network expansion or shrinking. [ABSTRACT FROM AUTHOR]

We study the statistical mechanics of binary systems under the gravitational interaction of the Modified Newtonian Dynamics (MOND) in three-dimensional space. Considering the binary systems in the microcanonical and canonical ensembles, we show that in the microcanonical systems, unlike the Newtonian gravity, there is a sharp phase transition, with a high-temperature homogeneous phase and a low-temperature clumped binary one. Defining an order parameter in the canonical systems, we find a smoother phase transition and identify the corresponding critical temperature in terms of the physical parameters of the binary system. [ABSTRACT FROM AUTHOR]

The combination of flexibility and semiflexibility in a single molecule is a powerful design principle both in nature and in materials science. We present results on the conformational behavior of a single multiblock-copolymer chain, consisting of equal amounts of Flexible (F) and Semiflexible (S) blocks with different affinity to an implicit solvent. We consider a manifold of macrostates defined by two terms in the total energy: intermonomer interaction energy and stiffness energy. To obtain diagrams of states (pseudo-phase diagrams), we performed flat-histogram Monte Carlo simulations using the Stochastic Approximation Monte Carlo algorithm (SAMC). We have accumulated two-Dimensional Density of States (2D DoS) functions (defined on the 2D manifold of macrostates) for a SF-multiblock-copolymer chain of length N = 64 with block lengths b = 4, 8, 16, and 32 in two different selective solvents. In an analysis of the canonical ensemble, we calculated the heat capacity and determined its maxima and the most probable morphologies in different regions of the state diagrams. These are rich in various, non-trivial morphologies, which are formed without any specific interactions, and depend on the block length and the type of solvent selectivity (preferring S or F blocks, respectively). We compared the diagrams with those for the non-selective solvent and reveal essential changes in some cases. Additionally, we implemented microcanonical analysis in the "conformational" microcanonical ( N V U , where U is the potential energy) and the true microcanonical ( N V E , where E is the total energy) ensembles with the aim to reveal and classify pseudo-phase transitions, occurring under the change of temperature. [ABSTRACT FROM AUTHOR]

The concept of the out-of-time-ordered correlation (OTOC) function is treated as a very strong theoretical probe of quantum randomness, using which one can study both chaotic and non-chaotic phenomena in the context of quantum statistical mechanics. In this paper, we define a general class of OTOC, which can perfectly capture quantum randomness phenomena in a better way. Further, we demonstrate an equivalent formalism of computation using a general time-independent Hamiltonian having well-defined eigenstate representation for integrable Supersymmetric quantum systems. We found that one needs to consider two new correlators apart from the usual one to have a complete quantum description. To visualize the impact of the given formalism, we consider the two well-known models, viz. Harmonic Oscillator and one-dimensional potential well within the framework of Supersymmetry. For the Harmonic Oscillator case, we obtain similar periodic time dependence but dissimilar parameter dependences compared to the results obtained from both microcanonical and canonical ensembles in quantum mechanics without Supersymmetry. On the other hand, for the One-Dimensional PotentialWell problem, we found significantly different time scales and the other parameter dependence compared to the results obtained from non-Supersymmetric quantum mechanics. Finally, to establish the consistency of the prescribed formalism in the classical limit, we demonstrate the phase space averaged version of the classical version of OTOCs from a model-independent Hamiltonian, along with the previously mentioned well-cited models. [ABSTRACT FROM AUTHOR]

Graphene-copper nanolayered composites have received research interest as promising packaging materials in developing next-generation electronic and optoelectronic devices. The weak van der Waal (vdW) contact between graphene and metal matrix significantly reduces the mechanical performance of such composites. The current study describes a new Cu-nanoporous graphene-Cu based bonding method with a low bonding temperature and good dependability. The deposition of copper atoms onto nanoporous graphene can help to generate nanoislands on the graphene surface, facilitating atomic diffusion bonding to bulk copper bonding surfaces at low temperatures, according to our extensive molecular dynamics (MD) simulations on the bonding process and pull-out verification using the canonical ensemble (NVT). Furthermore, the interfacial mechanical characteristics of graphene/Cu nanocomposites can be greatly improved by the resistance of nanostructure in nanoporous graphene. These findings are useful in designing advanced metallic surface bonding processes and graphene-based composites with tenable performance. [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 study of the human psyche has elucidated a bipartite structure of logic reflecting the quantum–classical nature of the world. Accordingly, we posited an approach toward studying the brain by means of the quantum–classical dynamics of a mixed Weyl symbol. The mixed Weyl symbol can be used to describe brain processes at the microscopic level and, when averaged over an appropriate ensemble, can provide a link to the results of measurements made at the meso and macro scale. Within this approach, quantum variables (such as, for example, nuclear and electron spins, dipole momenta of particles or molecules, tunneling degrees of freedom, and so on) can be represented by spinors, whereas the electromagnetic fields and phonon modes can be treated either classically or semi-classically in phase space by also considering quantum zero-point fluctuations. Quantum zero-point effects can be incorporated into numerical simulations by controlling the temperature of each field mode via coupling to a dedicated Nosé–Hoover chain thermostat. The temperature of each thermostat was chosen in order to reproduce quantum statistics in the canonical ensemble. In this first paper, we introduce a general quantum–classical Hamiltonian model that can be tailored to study physical processes at the interface between the quantum and the classical world in the brain. While the approach is discussed in detail, numerical calculations are not reported in the present paper, but they are planned for future work. Our theory of brain dynamics subsumes some compatible aspects of three well-known quantum approaches to brain dynamics, namely the electromagnetic field theory approach, the orchestrated objective reduction theory, and the dissipative quantum model of the brain. All three models are reviewed. [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]

Broadly distributed random variables with a power-law distribution f (m) ~ m -(1+α) are known to generate condensation effects. This means that, when the exponent a lies in a certain interval, the largest variable in a sum of N (independent and identically distributed) terms is for large N of the same order as the sum itself. In particular, when the distribution has infinite mean (0 < α < 1) one finds unconstrained condensation, whereas for α > 1 constrained condensation takes places fixing the total mass to a large enough value ... > Mc. In both cases, a standard indicator of the condensation phenomenon is the participation ratio ..., which takes a finite value for N → ∞ when condensation occurs. To better understand the connection between constrained and unconstrained condensation, we study here the situation when the total mass is fixed to a superextensive value M ~ N 1+ δ (δ > 0), hence interpolating between the unconstrained condensation case (where the typical value of the total mass scales as M ~ N1/α for α < 1) and the extensive constrained mass. In particular we show that for exponents a < 1 a condensate phase for values δ > δc = 1/α - 1 is separated from a homogeneous phase at δ < δc from a transition line, δ = δc, where a weak condensation phenomenon takes place. We focus on the evaluation of the participation ratio as a generic indicator of condensation, also recalling or presenting results in the standard cases of unconstrained mass and of fixed extensive mass. [ABSTRACT FROM AUTHOR]

Till now, kinetic theory and statistical mechanics of either free or interacting point particles were well defined only in non-relativistic inertial frames in the absence of the long-range inertial forces present in accelerated frames. As shown in the introductory review at the relativistic level, only a relativistic kinetic theory of "world-lines" in inertial frames was known till recently due to the problem of the elimination of the relative times. The recent Wigner-covariant formulation of relativistic classical and quantum mechanics of point particles required by the theory of relativistic bound states, with the elimination of the problem of relative times and with a clarification of the notion of the relativistic center of mass, allows one to give a definition of the distribution function of the relativistic micro-canonical ensemble in terms of the generators of the Poincaré algebra of a system of interacting particles both in inertial and in non-inertial rest frames. The non-relativistic limit allows one to get the ensemble in non-relativistic non-inertial frames. Assuming the existence of a relativistic Gibbs ensemble, also a "Lorentz-scalar micro-canonical temperature" can be defined. If the forces between the particles are short range in inertial frames, the notion of equilibrium can be extended from them to the non-inertial rest frames, and it is possible to go to the thermodynamic limit and to define a relativistic canonical temperature and a relativistic canonical ensemble. Finally, assuming that a Lorentz-scalar one-particle distribution function can be defined with a statistical average, an indication is given of which are the difficulties in solving the open problem of deriving the relativistic Boltzmann equation with the same methodology used in the non-relativistic case instead of postulating it as is usually done. There are also some comments on how it would be possible to have a hydrodynamical description of the relativistic kinetic theory of an isolated fluid in local equilibrium by means of an effective relativistic dissipative fluid described in the Wigner-covariant framework. [ABSTRACT FROM AUTHOR]

An important yet perplexing result from work in the 1990s and 2000s is the near-unity value of the ratio of fluctuations in the vacuum energy density of quantum fields to the mean in a collection of generic spacetimes. This was carried out by way of calculating the noise kernels which are the correlators of the stress-energy tensor of quantum fields. In this paper, we revisit this issue via a quantum thermodynamics approach, by calculating two quintessential thermodynamic quantities: the heat capacity and the quantum compressibility of some model geometries filled with a quantum field at high and low temperatures. This is because heat capacity at constant volume gives a measure of the fluctuations of the energy density to the mean. When this ratio approaches or exceeds unity, the validity of the canonical distribution is called into question. Likewise, a system's compressibility at constant pressure is a criterion for the validity of grand canonical ensemble. We derive the free energy density and, from it, obtain the expressions for these two thermodynamic quantities for thermal and quantum fields in 2d Casimir space, 2d Einstein cylinder and 4d ( S 1 × S 3 ) Einstein universe. To examine the dependence on the dimensionality of space, for completeness, we have also derived these thermodynamic quantities for the Einstein universes with even-spatial dimensions: S 1 × S 2 and S 1 × S 4 . With this array of spacetimes we can investigate the thermodynamic stability of quantum matter fields in them and make some qualitative observations on the compatibility condition for the co-existence between quantum fields and spacetimes, a fundamental issue in the quantum and gravitation conundrum. [ABSTRACT FROM AUTHOR]

We investigate the stationary and dynamic properties of the celebrated Nosé--Hoover dynamics of many-body interacting Hamiltonian systems, with an emphasis on the effect of inter-particle interactions. To this end, we consider a model system with both short- and long-range interactions. The Nosé--Hoover dynamics aim to generate the canonical equilibrium distribution of a system at a desired temperature by employing a set of time-reversible, deterministic equations of motion. A signature of canonical equilibrium is a single-particle momentum distribution that is Gaussian. We find that the equilibrium properties of the system within the Nosé--Hoover dynamics coincides with that within the canonical ensemble. Moreover, starting from out-of-equilibrium initial conditions, the average kinetic energy of the system relaxes to its target value over a size-independent timescale. However, quite surprisingly, our results indicate that under the same conditions and with only long-range interactions present in the system, the momentum distribution relaxes to its Gaussian form in equilibrium over a scale that diverges with the system size. On adding short-range interactions, the relaxation is found to occur over a timescale that has a much weaker dependence on system size. This system-size dependence of the timescale vanishes when only short-range interactions are present in the system. An implication of such an ultra-slow relaxation when only long-range interactions are present in the system is that macroscopic observables other than the average kinetic energy when estimated in the Nosé--Hoover dynamics may take an unusually long time to relax to its canonical equilibrium value. Our work underlines the crucial role that interactions play in deciding the equivalence between Nosé--Hoover and canonical equilibrium. [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]