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Many models with long-range interactions, including the Nagel-Kardar (NK) model, have been proposed to demonstrate and explore the differences between microcanonical ensembles and canonical ensembles. In the NK model, the first-order phase transition always accompanied by the temperature jump in the microcanonical ensemble, while this anomalous temperature jump can not be observed in the canonical ensemble. Moreover, the tricritical points of this model are different from each other in these two different ensembles. In this paper, the microcanonical-canonical crossover behavior of the NK model is studied by placing the NK model in contact with a two-level reservoir, and transition of the tricritical point is presented.

We have studied analytically the persistent current and the magnetization of two electrons trapped by a circular parabolic GaAs quantum dot using the canonical ensemble approach. We have investigated their behavior as a function of the dot size and magnetic field in the presence and the absence of the harmonic e–e interaction at high and low temperatures. Our investigations reveal that the diamagnetic state is the preferred state for the persistent current and magnetization. As a function of the dot size, initially the current is entirely independent of the interaction and it remains constant up to a certain value of the dot size beyond which it increases significantly and the effect of the harmonic interaction becomes tangible in the low-temperature limit. However as a function of the magnetic field at high temperatures, the current takes a diminishing linear form and this decrease is noticeable for narrower dots, but at extremely low temperatures, the current becomes insensitive to the interaction for a dot with small size. As a function of temperature, the current increases sharply with temperature and then tends to saturate as the temperature becomes slightly larger. This study demonstrates a comparison between the current and the magnetization. Our results show that, as a function of temperature, they qualitatively exhibit the same behavior and they are proportional to each other in the presence of weak magnetic field, while as a function of the magnetic field, they display non-similar behavior at low temperatures.

We examine the minimization of information entropy for measures on the phase space of bounded domains, subject to constraints that are averages of grand canonical distributions. We describe the set of all such constraints and show that it equals the set of averages of all probability measures absolutely continuous with respect to the standard measure on the phase space (with the exception of the measure concentrated on the empty configuration). We also investigate how the set of constrains relates to the domain of the microcanonical thermodynamic limit entropy. We then show that, for fixed constraints, the parameters of the corresponding grand canonical distribution converge, as volume increases, to the corresponding parameters (derivatives, when they exist) of the thermodynamic limit entropy. The results hold when the energy is the sum of any stable, tempered interaction potential that satisfies the Gibbs variational principle (e.g.~Lennard-Jones) and the kinetic energy. The same tools and the strict convexity of the thermodynamic limit pressure for continuous systems (valid whenever the Gibbs variational principle holds) give solid foundation to the folklore local homeomorphism between thermodynamic and macroscopic quantities., Comment: Section 2 revised and improved. The rest of the article has been rewritten accordingly. 22 pages, 2 figures

Using canonical ensemble, we have studied the magnetic properties of a cylindrical GaAs quantum dot in this paper. The system is under the direct influence of external static electric and magnetic fields and an Aharonov-Bohm magnetic flux. Considering the temperature- and pressure-dependent effective parameters, the magnetic susceptibility is calculated and plotted in different regimes. Results clearly show the magnetic susceptibility, magnetic transition, and critical points strongly depend on temperature, pressure, and magnetic field. Moreover, Aharonov-Bohm magnetic flux has considerable effects on the magnetic susceptibility of the system.

In this work, we have studied the thermodynamic properties of a GaAs quantum dot (QD) with an effective-parabolic potential. We have analytically obtained entropy, heat capacity and average energy of the QD in the presence of a magnetic field and its interaction with the electron spin using the canonical ensemble approach. According to the results, it is found that the entropy is an increasing function of temperature. At low temperatures, the entropy increases monotonically with increasing the temperature for all values of the magnetic field and it is independent of the magnetic field. But, the entropy depends on the magnetic field at high temperatures. The entropy is also decreased with increasing magnetic field. The average energy of the system is increased by enhancing temperature and magnetic field. At low temperatures, the average energy appears weakly dependent on magnetic field. It is nearly independent of magnetic field. The heat capacity increases with enhancing temperatures for all considered values of magnetic fields, and it approaches a saturation value at high temperatures. The heat capacity decreases with increasing the magnetic field for all considered values of temperatures. There is an interesting behavior in heat capacity as a function of magnetic field. The heat capacity does not change much at high temperatures like T = 200 K and 300 K. However, at relatively lower temperatures like T = 100 K, the heat capacity reduces with increasing magnetic field. We have also calculated the magnetization of the system. The magnitude of the magnetization $$ \left( {\left| M \right|} \right) $$ increases with the magnetic field and the confinement range.

We consider a one-dimensional lattice system of unbounded, real-valued spins with arbitrary strong, quadratic, finite-range interaction. We show the equivalence of correlations of the grand canonical (gce) and the canonical ensemble (ce). As a corollary we obtain that the correlations of the ce decay exponentially plus a volume correction term. Then, we use the decay of correlation to verify a conjecture that the infinite-volume Gibbs measure of the ce is unique on a one-dimensional lattice. For the equivalence of correlations, we modify a method that was recently used by the authors to show the equivalence of the ce and the gce on the level of thermodynamic functions. In this article we also show that the equivalence of the ce and the gce holds on the level of observables. One should be able to extend the methods and results to graphs with bounded degree as long as the gce has a sufficient strong decay of correlations., Comment: 28 pages

The operator of time formalism is applied to radioactive decay. It appears that the proposed approach offers a better insight and understanding of the phenomena in a way that the decay exponential-law becomes the Boltzmann distribution in Gibbs treatment of canonical ensemble. The radioactive decay is seen as temporal canonical ensemble where the radioactive constant appears as the analog of the absolute temperature multiplied by Boltzmann constant. The stochastic character of decay process becomes plausible in the proposed approach and the explanation why decay is characterized by fixed quantity, and not by some parameter, is offered.

Statistical models of a single open string avoiding self-intersections in the d-dimensional Euclidean space ℝd, 2 ≤ d < 4, and the ensemble of strings are considered. The presentation of these models is based on the Darwin–Fowler method, used in statistical mechanics to derive the canonical ensemble. The configuration of the string in space ℝd is described by its contour length L and the spatial distance R between its ends. We establish an integral equation for a transformed probability density W(R, L) of the distance R similar to the known Dyson equation, which is invariant under the continuous group of renormalization transformations. This allows us using the renormalization group method to investigate the asymptotic behavior of this density in the case where R → ∞ and L → ∞. For the model of an ensemble of M open strings with the mean string contour length over the ensemble given by $$ \overline{L} $$ , we obtain the most probable distribution of strings over their lengths in the limit as M → ∞. Averaging the probability density W(R, L) over the canonical ensemble eventually gives the sought density 〈W(R, L)〉.

We make a theoretical and experimental summary of the state-of-the-art status of hot and dense QCD matter studies on selected topics. We review the Beam Energy Scan program for the QCD phase diagram and present the current status of the search for the QCD critical point, particle production in high baryon density region, hypernuclei production, and global polarization effects in nucleus-nucleus collisions. The available experimental data in the strangeness sector suggests that a grand canonical approach in the thermal model at high collision energy makes a transition to the canonical ensemble behavior at low energy. We further discuss future prospects of nuclear collisions to probe properties of baryon-rich matter. Creation of a quark-gluon plasma at high temperature and low baryon density has been called the “Little-Bang” and, analogously, a femtometer-scale explosion of baryon-rich matter at lower collision energy could be called the “femto-nova”, which could possibly sustain substantial vorticity and a magnetic field for non-head-on collisions.

Monte Carlo simulations have boosted the numerical study of several different physical systems and in particular, the canonical ensemble has been especially useful because of the existence of easy and efficient simulation algorithms. Nevertheless, nature does not know about statistical ensembles and therefore it is desirable and a theoretical challenge to show how to perform numerical simulations in the microcanonical ensemble without the use of unphysical degrees of freedom. In this article, we present a straightforward applicable method based on the concepts of a configurational temperature estimator (Rugh Phys Rev Lett 78:772, 1997; Gutierrez et al. J Phys A Math Theor 51:455003, 2018) and on stochastic dynamics, which is independent of the Monte Carlo update strategy, and can be implemented for both local update or cluster algorithms. We illustrate it by performing a numerical simulation of the two-dimensional XY-model, finding the equilibrium temperature of two spin subsystems initially at different temperatures when they are put into thermal contact.

Schrodinger equation with position-dependent mass (PDM) allows the identification of quantum wave functions in a complex environment. Following the progress of this investigation field, in this work, we consider the non-Hermitian kinetic operators associated with the PDM Schrodinger equation. We provide a simplified picture for PDM quantum systems that admit exact solutions in confining potentials. First, we investigate the solutions for a sinusoidal and an exponential PDM distributions in an infinite potential well. Next, we consider the solutions for a PDM harmonic oscillator potential associated with a power-law PDM distribution. The results presented in this work offer a way to approach new classes of solutions for PDM quantum systems in confining potential (bound states). Complementarily, we interpret the quantum partition function of the canonical ensemble of a PDM system in the context of the superstatistics, which, in turn, allows us to express the inhomogeneity of the PDM in terms of beta distribution $$f(\beta )$$ , Dirac delta distributions for $$f(\beta )$$ , and effective temperatures. Our results are, hereby, reported for the sinusoidal and the exponential PDM distributions.

We find a family of complex saddle-points at large N of the matrix model for the superconformal index of SU(N ) $$ \mathcal{N} $$ N = 4 super Yang-Mills theory on S3× S1 with one chemical potential τ . The saddle-point configurations are labelled by points (m, n) on the lattice Λτ = ℤτ + ℤ with gcd(m, n) = 1. The eigenvalues at a given saddle are uniformly distributed along a string winding (m, n) times along the (A, B) cycles of the torus ℂ/Λτ . The action of the matrix model extended to the torus is closely related to the Bloch-Wigner elliptic dilogarithm, and the related Bloch formula allows us to calculate the action at the saddle-points in terms of real-analytic Eisenstein series. The actions of (0, 1) and (1, 0) agree with that of pure AdS5 and the supersymmetric AdS5 black hole, respectively. The black hole saddle dominates the canonical ensemble when τ is close to the origin, and there are new saddles that dominate when τ approaches rational points. The extension of the action in terms of modular forms leads to a simple treatment of the Cardy-like limit τ → 0.

We discuss the effects of the recently proposed generalized (anti-)Snyder model on the thermostatistics of a classical ideal gas in the canonical ensemble and the blackbody energy spectrum. In the framework of this modified algebra, we calculate the modified partition function exactly and derive all thermodynamic quantities. The results show that the effects of the generalized (anti-)Snyder model become important only at the very high-temperature regime.

A long-range interacting spin chain placed in a staggered magnetic field can exhibit either first order phase transition or second order phase transition depending on the magnetic field intensity. The first order phase transition of this model is known to be accompanied with the temperature jump phenomenon in the microcanonical ensemble, while this anomalous temperature jump phenomenon can not be observed in the canonical ensemble. We obtain the crossover phase transition properties passing from a microcanonical to a canonical ensemble, by placing this previously isolated spin chain model in contact with a two-level system that acts as a thermal reservoir. The magnitude of the temperature jump monotonically decreases with the increase of the size of the thermal reservoir. And the microcanonical phase diagram can gradually turn into the canonical phase diagram by increasing the number of particles of the reservoir.

In the present paper, the thermodynamics of three-dimensional impurity magnetopolaron under strong parabolic potential is investigated. To this aim, we first analytically solved the Schrodinger equation to have the complete energy spectrum in the presence of spin–orbit interaction. We equally use the canonical ensemble approach to obtain the partition function before calculating the thermodynamic parameters. Afterward, we found a great dependence of those thermodynamic parameters such as entropy and heat capacity on spin–orbit interaction (SOI). From this investigation, we found that there are some particular values of SOI for which we have a minimum values reached by the entropy as well as in the presence of magnetic field than temperature. This study allows us to conclude that SOI is a very useful parameter in order to build stable quantum system.

In this work, we performed a theoretical density functional theory (DFT) and semi-empirical (PM3) analysis to calculate thermodynamic properties of biokerosene from coconut and palm kernel oils, Jet Propulsion Fuel 8 (JP-8), and mixtures of these fuels. All simulations were performed in thermal equilibrium and for a temperature range of 0.5-1500 K, considering the canonical ensemble model. We predicted the thermal properties energy, enthalpy, enthalpy change, Gibbs free energy, entropy, and specific heat at constant pressure with respect to temperature. In addition, we compared the performances of the DFT functional hybrid B3LYP and the basis set 6-311++G(d,p) and PM3 methods, in order to determine their accuracy for thermodynamic predictions relating to the fuels. Calculations for combustion enthalpy were carried out using the following methods: B3LYP/6-311++G(d,p), B3LYP/6-31+G(d), CBS-QB3, G3, G4, and G3/G4. The results showed good agreement with measured values, indicating that DFT may be a good method to calculate and predict thermodynamic properties of the combustion reactions of kerosene and biokerosene.

The reflection operators are the simplest examples of the non-local integrals of motion, which appear in many interesting problems in integrable CFT. For the so-called Fateev, quantum AKNS, paperclip and KdV integrable structures, they are built from the (chiral) reflection S-matrices for the Liouville and cigar CFTs. Here we give the full spectrum of the reflection operators associated with these integrable structures. We also obtained a relation between the reflection S-matrices of the cigar and Liouville CFTs. The results of this work are applicable for the description of the scaling behaviour of the Bethe states in exactly solvable lattice systems and may be of interest to the study of the Generalized Gibbs Ensemble associated with the above mentioned integrable structures., Comment: 33 pages, published version

In this paper, we investigate the thermodynamic properties of a set of neutral Dirac particles in the presence of an electromagnetic field in contact with a heat bath for the relativistic and nonrelativistic cases. In order to perform the calculations, the high temperatures regime is considered and the Euler–MacLaurin formula is taking into account. Next, we explicitly determine the behavior of the main thermodynamic functions of the canonical ensemble: the Helmholtz free energy, the mean energy, the entropy, and the heat capacity. As a result, we verify that the mean energy and the heat capacity for the relativistic case are twice the values of the nonrelativistic case, thus, satisfying the so-called Dulong–Petit law. In addition, we also verify that the Helmholtz free energy increases and the entropy decreases as functions of the electric field. Finally, we note that there exists no influence on the thermodynamic functions due to the magnetic field.

For a random graph subject to a topological constraint, the microcanonical ensemble requires the constraint to be met by every realisation of the graph (`hard constraint'), while the canonical ensemble requires the constraint to be met only on average (`soft constraint'). It is known that breaking of ensemble equivalence may occur when the size of the graph tends to infinity, signalled by a non-zero specific relative entropy of the two ensembles. In this paper we analyse a formula for the relative entropy of generic discrete random structures recently conjectured by Squartini and Garlaschelli. We consider the case of a random graph with a given degree sequence (configuration model), and show that in the dense regime this formula correctly predicts that the specific relative entropy is determined by the scaling of the determinant of the matrix of canonical covariances of the constraints. The formula also correctly predicts that an extra correction term is required in the sparse regime and in the ultra-dense regime. We further show that the different expressions correspond to the degrees in the canonical ensemble being asymptotically Gaussian in the dense regime and asymptotically Poisson in the sparse regime (the latter confirms what we found in earlier work), and the dual degrees in the canonical ensemble being asymptotically Poisson in the ultra-dense regime. In general, we show that the degrees follow a multivariate version of the Poisson-Binomial distribution in the canonical ensemble., Journal of Statistical Physics, (), 1-19

Interatomic potentials for complex materials (like ceramic systems) are important for realistic molecular dynamics (MD) simulations. Such simulations are relevant for understanding equilibrium, transport and dynamical properties of materials, especially in the nanoregime. Here we derive a hybrid interatomic potential (based on bond valence (BV) derived Morse and Coulomb terms), for modeling a complex ceramic, barium tantalum oxynitride (BaTaO2N). This material has been chosen due to its relevance for capacitive and photoactive applications. However, the material presents processing challenges such as the emergence of non-stoichiometric phases during processing, demonstrating complex processing–property correlations. This makes MD investigations of this material both scientifically and technologically relevant. The BV based hybrid potential presented here has been used for simulating sintering of BaTaO2N nanoparticles (~ 2–20 nm) under different conditions (using the relevant canonical ensemble). Notably, we show that sintering of particles of diameter 10 nm in size results in the formation of a cluster of tantalum and oxygen atoms at the interface of the BaTaO2N particles. This is in agreement with the experimental reports. The results presented here suggest that the potential proposed can be used to explore dynamical properties of BaTaO2N and related systems. This work will also open avenues for development of nanoscience-enabled aid-free sintering approaches to this and related materials.

Motivated by recent experiments with two-component Bose-Einstein condensates, we study fully-connected spin models subject to an additional constraint. The constraint is responsible for the Hilbert space dimension to scale only linearly with the system size. We discuss the unconventional statistical physical and thermodynamic properties of such a system, in particular the absence of concentration of the underlying probability distributions. As a consequence, expectation values are less suitable to characterize such systems, and full distribution functions are required instead. Sharp signatures of phase transitions do not occur in such a setting, but transitions from singly peaked to doubly peaked distribution functions of an "order parameter" may be present., 15 pages, 6 figures

We prove absolute convergence of the multi-body correlation functions as a power series in the density uniformly in their arguments. This is done by working in the context of the cluster expansion in the canonical ensemble and by expressing the correlation functions as the derivative of the logarithm of an appropriately extended partition function. In the thermodynamic limit, due to combinatorial cancellations, we show that the coefficients of the above series are expressed by sums over some class of two-connected graphs. Furthermore, we prove the convergence of the density expansion of the “direct correlation function” which is based on a completely different approach and it is valid only for some integral norm. Precisely, this integral norm is suitable to derive the Ornstein–Zernike equation. As a further outcome, we obtain a rigorous quantification of the error in the Percus–Yevick approximation.

International audience; We study the equivalence of microcanonical and canonical ensembles in continuous systems, in the sense of the convergence of the corresponding Gibbs measures and the first order corrections. We are particularly interested in extensive observables, like the total kinetic energy. This result is obtained by proving an Edgeworth expansion for the local central limit theorem for the energy in the canonical measure, and a corresponding local large deviations expansion. As an application we prove a formula due to Lebowitz-Percus-Verlet that express the asymptotic microcanonical variance of the kinetic energy in terms of the heat capacity.

The water present in all gas stream leads to changes in the adsorbed amount of the target gas and the selectivity among the constituents of the mixture. The high stability characteristics and low cost of the new Al(OH) fumarate MOF synthetized by BASF, makes it an interesting porous material with mild hydrophobic properties for industrial use. Thus, new force field parameters were proposed for the CO2, N2 and CH4 /Al(OH) fumarate systems validated by adsorption experimental data in three temperatures. The sittings of CO2, N2, CH4 and H2O molecules inside the MOF pores at high (303 K) and low (150 K or 230 K) temperatures were also presented. An alternative approach that performed Monte Carlo simulations on two ensembles, the canonical ensemble (NVT) and the grand canonical ensemble (µVT), was validated and applied to evaluate the coadsorption of CO2/H2O, N2/H2O and CH4/H2O for a MOF exposure to the relative humidity of 14, 20, 25, 30 and 40% at 303 K. The gases molecules fill the center of the pores of the Al(OH) fumarate MOF near the aluminum clusters. The water molecules showed a complex behavior, forming clusters even in the early stages of adsorption. The Al(OH)-fumarate MOF, when compared to NaX, shows hydrophobic behavior and impaired in CO2 capacity only at relative humidity above 20%. We also found that CO2 selectivity increases for CO2/N2 and CO2/CH4 as the amount of water increases. We hope that the proposed methodology to study water coadsorption could be applied to other frameworks to assist in the screening of MOF for separation/capture.

In this paper, a theoretical analysis of the kinetic properties of the isotropic conducting crystals is presented. The general formulas for these kinetic properties are expressed in terms of the Fermi integrals. These integrals were obtained using methods of statistical ensembles with varying number of particles and the Gibbs’s grand canonical distribution. The determination of the scattering function and the exploration of its relation with the mobility of the current carriers inside these crystals have been made. Together with the results of theoretical analysis of the scattering function and its relation with the current carriers’ mobility, these formulas constitute the mathematical model of the charge carriers’ transport phenomena in conducting crystals (where a non-parabolic energy spectrum is described by Kane’s formula) and provide algorithms for the calculation of these properties.

We study the thermodynamics of an exact hairy black hole solution in Anti-deSitter (AdS) spacetime. We use the counterterm method supplemented with boundary terms for the scalar field to obtain the thermodynamic quantities and stress tensor of the dual field theory. We then extend our analysis by considering a dynamical cosmological constant and verify the isoperimetric inequality. Unlike the thermodynamics of Reissner-N\"{o}rdstrom (RN) black hole in this `extended' framework, the presence of the scalar field and its self-interaction make also the criticality possible in the grand canonical ensemble. In the canonical ensemble, we prove that, in fact, there exist two critical points. Finally we comment on a different possible interpretation that is more natural in the context of string theory., Comment: 39 pages, 21 figures;v2: typos fixed, refs. added;v3: comments added

The action of the charged Einstein-dilaton gravity theory is obtained from that of the scalar-tensor gravity theory by use of the transformations defined as $ g_{\mu\nu}\rightarrow \Omega^{2}g_{\mu\nu}$ and $ A_{\mu}\rightarrow A_{\mu}$. It is shown that, under these conformal transformations, the Lagrangian of Maxwell’s electrodynamics remains invariant in four-dimensional space-times. The related field equations are solved in the framework of Einstein-dilaton theory, and the dilatonic potential is obtained as a linear combination of three Liouville-type potentials. Two classes of novel charged black holes are identified as the exact solution to the field equations of the Einstein-Maxwell-dilaton theory. We calculate the conserved and thermodynamic quantities of dilaton black holes and show that the first law of black hole thermodynamics is valid in its standard form. Also, the thermodynamic stability or the phase transition of dilaton black holes is analyzed by use of the canonical ensemble method. Then, making use of the inverse conformal transformations, two classes of charged scalar-tensor black holes are obtained from their Einstein-dilaton counterparts and their thermodynamic properties as well as thermodynamic phase transitions are investigated.

In this paper, we investigate the thermodynamic properties of an Aharonov-Bohm (AB) quantum ring in a heat bath for both relativistic and non-relativistic cases. For accomplishing this, we used the partition function which was obtained numerically using the Euler-Maclaurin formula. In particular, we determined the energy spectra as well as the behavior of the main thermodynamic functions of the canonical ensemble, namely, the Helmholtz free energy, the mean energy, the entropy and the heat capacity. The so-called Dulong-Petit law was verified only for the relativistic case. We noticed that in the low energy regime, the relativistic thermodynamic functions are reduced to the non-relativistic case as well., Comment: 12 pages, 8 figures

The nonextensive boson system is revisited with the statistical ensemble theory, where the fundamental grand canonical distribution is derived from the equiprobability principle. By recourse to the approach of parameter transformation, one familiar and concise statistical formula for bosons is deduced, in an accurate fashion. Then the Bose-Einstein condensation phenomenon is re-discussed. The results show that the critical temperature is dependent on the nonextensive parameter $ \nu$ , and in the generalized expression of the heat capacity for the condensated phase of boson systems there exists one additional term, obeying the T3 law. By use of the statistical formula, the nonextensive photon gas is also researched. The internal energy and heat capacity for the nonextensive photon gas exhibit a similar dependence on the temperature to the classical photon gas, apart from a coefficient correction dependent on the parameter $ \nu$ . The Gibbs function for the nonextensive photon gas is still zero, showing that the photon field is also at thermal equilibrium, like the situation of classical photon field. The entropy of photon field can be calculated through the integral of the nonextensive quantum statistics formula and can also be derived from the original definition of Tsallis entropy, by recourse to the direct parameter transformation. This seems to indicate the validity of the treatment technique for the nonextensive quantum systems.

Starting from the suitable action of four-dimensional Einstein-dilaton gravity with the logarithmic nonlinear electrodynamics, the explicit form of the coupled scalar, electromagnetic and gravitational field equations have been obtained. Through the exact solution of the field equations, the nonvanishing component of the electromagnetic tensor have been obtained and it has been shown that dilaton potential can be written as the suitable combination of two terms similar to the Liouville potentials. Three classes of novel electrically charged hairy black holes have been introduced with the regular and well-defined metric functions for all values of the parameters in the theory. The solutions reduce to their corresponding values in the Einstein-Maxwell-dilaton theory when the nonlinearity parameter of the electrodynamics goes to infinity. The thermodynamic quantities, such as temperature, entropy, mass, electric charge and electric potential, have been calculated and it has been demonstrated that the first law of black hole thermodynamics is valid for all of the new solutions. Thermodynamic stability or phase transition of the black holes have been investigated based on the canonical ensemble method. By calculating the black hole heat capacity type-1 and type-2 phase transition points have been determined. Also, it has been found that in order for the new nonlinearly charged dilaton black holes to remain locally stable some simple conditions must be fulfilled.

We discuss the thermodynamics of a general nonlinear electrodynamics (NLED) asymptotically flat black hole enclosed in a finite spherical cavity. A canonical ensemble is considered, which means that the temperature and the charge on the wall of the cavity are fixed. After the free energy is obtained by computing the Euclidean action, it shows that the first law of thermodynamics is satisfied at the locally stationary points of the free energy. Focusing on a Born-Infeld (BI) black hole in a cavity, the phase structure and transition in various regions of the parameter space are investigated. In the region where the BI electrodynamics has weak nonlinearities, Hawking-Page-like and van der Waals-like phase transitions occur, and a tricritical point appears. In the region where the BI electrodynamics has strong enough nonlinearities, only Hawking-Page-like phase transitions occur. The phase diagram of the BI black hole in a cavity can have dissimilarity from that of a BI black hole using asymptotically anti-de Sitter boundary conditions. The dissimilarity may stem from a lack of an appropriate reference state with the same charge and temperature for the BI-AdS black hole., 29 pages, 10 figures

The nonextensive statistical ensembles are revisited for the complex systems with long-range interactions and long-range correlations. An approximation, the value of nonextensive parameter (1-q) is assumed to be very tiny, is adopted for the limit of large particle number for most normal systems. In this case, Tsallis entropy can be expanded as a function of energy and particle number fluctuation, and thus the power-law forms of the generalized Gibbs distribution and grand canonical distribution can be derived. These new distribution functions can be applied to derive the free energy and grand thermodynamic potential in nonextensive thermodynamics. In order to establish appropriate nonextensive thermodynamic formalism, the dual thermodynamic interpretations are necessary for thermodynamic relations and thermodynamic quantities. By using a new technique of parameter transformation, the single-particle distribution can be deduced from the power-law Gibbs distribution. This technique produces a link between the statistical ensemble and the quasi-independent system with two kinds of nonextensive parameter having quite different physical explanations. Furthermore, the technique is used to construct nonextensive quantum statistics and effectively to avoid the factorization difficulty in the power-law grand canonical distribution., 26 pages, 48 references

The standard approach of the Bardeen-Cooper-Schrieffer (BCS) theory of superconductivity is to introduce a self-consistent mean-field approximation, and a variational ansatz for the many-body ground state. The resulting mean-field Hamiltonian no longer commutes with the total number operator, and the variational search takes place in Fock space rather than in a Hilbert space of states with fixed number of particles. This is a disadvantage when studying small systems where the canonical ensemble predictions differ from the corresponding grand-canonical results. To remedy this, alternative approaches such as Richardson's method have been put forward. Here, we derive the exact many-body ground state of a model Hamiltonian corresponding to the deep-BCS or flat-band regime, without having to resort to Richardson's set of coupled nonlinear equations. This allows to write the exact many-body ground state in a way that makes the difference with the BCS variational wave function particularly clear. We show that the exact wave function consists of a superposition of many-pair states in such a way that the mean-field averaging corresponds to a summation over these many-pair states. This explains why many expectation values calculated with the BCS variational wave function give the same result as when calculated with the exact wave function, even though these wave functions are different. In the canonical (fixed-number) approach, pairing is investigated using the second-order reduced density matrix and calculating its largest eigenvalue. When interpreted as the order parameter of the superconducting state, this can be compared directly to the behavior of the mean-field gap. Finally, we show that a clear difference between the canonical approach and the BCS grand canonical estimates appears when evaluating pair condensate fluctuations as well as the pair entanglement entropy.

In this paper, we study the two-dimensional Bose-Hubbard model with short- and long-range interactions in the canonical ensemble. Using a Variational Monte-Carlo method, we obtain the phase diagrams containing four different phases: Mott insulator, density wave, superfluid and supersolid. The transition lines are determined using the structure factor and the superfluid density. We observe that the phase diagrams for short and long-range interactions are very similar quantitatively and qualitatively, but show also some significant differences. To evaluate the quality of our Variational approach, we compare our results with results published by other groups, obtained with various methods, such as an exact quantum Monte-Carlo algorithm and Gutzwiller Ansatz.

The selection and design of an optimal solvent for extractive distillation require reliable vapour–liquid phase equilibrium data and knowledge of extraction mechanisms. Compared with time-consuming experiments, molecular simulation presents great potential in research on the properties of fluids. Therefore, in this work, Gibbs ensemble Monte Carlo was applied to successfully predict the vapour–liquid phase equilibrium data of binary and ternary systems containing benzene, thiophene and N, N-dimethylformamide (DMF) at P = 101.3 kPa. The explicit hydrogen version of the transferable potentials for phase equilibria potential model was chosen for benzene and thiophene, whereas the OPLS potential model was selected for DMF. The predicted phase diagrams were compared with experimental data and the UNIQUAC thermodynamic model. A good agreement was obtained, which corroborated the validity of the potential models. In addition, the extraction mechanism was explored by radial distribution function (RDF) of the liquid-phase structure. The RDFs showed that thiophene and benzene shared a similar liquid-phase structure because of the intermolecular interaction. The distinct difference between the RDFs of DMF/benzene and those of DMF/thiophene is that the oxygen atom of DMF is more associated with hydrogen atoms of thiophene than that of benzene, which may be responsible for the extraction effect of DMF.

Using the classical Heisenberg model and Monte Carlo simulations in the canonical ensemble, the effect of form, finite-size, and surface roughness on magnetization is investigated for ferromagnetic nanoparticle with uniaxial anisotropy and different nanoparticle shapes. In this work, cubical and spherical nanoparticles are considered; we have considered a simple nanoparticle where each site is occupied by a classical Heisenberg spin. Our numerical results show that the nanoparticle size and surface roughness have an impact and a considerable influence on the magnetic properties of these nanoparticles. But the influence of nanoparticle shapes is less significant when comparing magnetic behavior for cubical and spherical forms of the particle in a smooth or rough surface.

The finite-size effects of the surface tension in two segregated Bose–Einstein condensates limited by two hard walls are studied respectively in canonical ensemble and grand canonical ensemble by means of the Gross–Pitaevskii theory in the modified double-parabola approximation. The analytical formulae of surface tensions and their finite-size effects are found together with a new type of long-range forces acting on two walls.

The properties of uranium hexafluoride (UF6, CAS: 7783-81-5) are of importance to the nuclear industry as a precursor for the enrichment and product spent fuel reprocessing. This work is focused on obtaining the vapor–liquid equilibrium (VLE) curve for UF6 using temperature dependent intermolecular potential parameters (TDIP) as opposed to temperature independent intermolecular potential parameters (TIIP). TDIP indeed improves the simulated vapor–liquid coexistence curve, critical constants, and vapor pressure of UF6. However, both approaches need improvement since the predictions are still far from reproducing experimental saturated liquid density data for UF6.

In this article, the new black hole solutions to the Einstein-power-Maxwell-dilaton gravity theory have been investigated in a three-dimensional space time. The coupled scalar, electromagnetic and gravitational field equations have been solved in a spherically symmetric geometry and it has been shown that the dilatonic potential, as the solution to the scalar field equation, can be written in the form of a generalized Liouville potential. Also, two new classes of charged dilatonic BTZ black hole solutions, in the presence of power-law nonlinear electrodynamics, have been constructed out which are asymptotically non-flat and non-AdS. The conserved and thermodynamic quantities have been calculated from geometrical and thermodynamical approaches, separately. The consistency of the results of these two alternative approaches confirms the validity of the first law of black hole thermodynamics for both of the new black hole solutions. The black holes stability or phase transitions have been studied, making use of the canonical ensemble method. The points of type one and type two phase transitions as well as the ranges at which the black holes are stable have been indicated by considering the heat capacity of the new black hole solutions.

A quantum analysis was performed with Density Functional Theory and a canonical ensemble, in order to predict thermodynamic properties of gasoline with additives at the gas phase. These calculated quantities included standard gasoline mixed with the following oxygenate additives: methyl tert-butyl ether, ethyl tert-butyl ether, diisopropyl ether, ethanol and methanol. For each gasoline and additive mixture, thermodynamic potential variations were calculated between room and the approximate ignition temperatures at 1 atm, where an analysis of the additive effect was performed in order to estimate relevant fuel properties at similar conditions to the injection step and combustion. Some thermodynamic quantities for combustion were obtained, showing substantial concordance with experimental data, relative errors being lower than 2%, thus establishing an excellent method for calculating and predicting the thermodynamic properties of combustion reactions for gasoline with additives.

In this work, we investigate the heat exchange between two quantum systems whose initial equilibrium states are described by the generalized Gibbs ensemble. First, we generalize the fluctuation relations for heat exchange discovered by Jarzynski and W\'ojcik to quantum systems prepared in the equilibrium states described by the generalized Gibbs ensemble at different generalized temperatures. Second, we extend the connections between heat exchange and R\'enyi divergences to quantum systems with very general initial conditions.These relations are applicable for quantum systems with conserved quantities and are universally valid for quantum systems in the integrable and chaotic regimes., Comment: 7 pages

We perform molecular dynamics simulations of Lennard–Jones particles in a canonical ensemble to study the diffusion of nanodroplets on smooth solid surfaces. Using the droplet-surface interaction to realize a hydrophilic or hydrophobic surface and calculating the mean square displacement of the center-of-mass of the nanodroplets, the random motion of nanodroplets could be characterized by shorttime subdiffusion, intermediate-time superdiffusion, and long-time normal diffusion. The short-time subdiffusive exponent increases and almost reaches unity (normal diffusion) with decreasing droplet size or enhancing hydrophobicity. The diffusion coefficient of the droplet on hydrophobic surfaces is larger than that on hydrophilic surfaces.

In this paper, we study the T -fluctuated form of superstatistics. In this form, some thermodynamic quantities such as the Helmholtz energy, the entropy and the internal energy, are expressed in terms of the T -fluctuated form for a canonical ensemble. In addition, the partition functions in the formalism for 2-level and 3-level distributions are derived. Then we make use of the T -fluctuated superstatistics for a quantum harmonic oscillator problem and the thermal properties of the system for three statistics of the Bose-Einstein, Maxwell-Boltzmann and Fermi-Dirac statistics are calculated. The effect of the deformation parameter on these properties is examined. All the results recover the well-known results by removing the deformation parameter.

We construct generalized grand-canonical- and canonical Gibbs measures for a Hamiltonian system described in terms of a complex scalar field that is defined on a circle and satisfies a nonlinear Schrodinger equation with a focusing nonlinearity of order p < 6. Key properties of these Gibbs measures, in particular absence of “phase transitions” and regularity properties of field samples, are established. We then study a time evolution of this system given by the Hamiltonian evolution perturbed by a stochastic noise term that mimics effects of coupling the system to a heat bath at some fixed temperature. The noise is of Ornstein–Uhlenbeck type for the Fourier modes of the field, with the strength of the noise decaying to zero, as the frequency of the mode tends to ∞. We prove exponential approach of the state of the system to a grand-canonical Gibbs measure at a temperature and “chemical potential” determined by the stochastic noise term.

We find a self-similar analytical solution for the grand-canonical-ensemble (GCE) statistics and thermodynamics in the critical region of Bose–Einstein condensation. It is valid for an arbitrary trap, loaded with an ideal gas, in the thermodynamic limit. We show that for the quantities, changing by a finite amount across the critical region, the exact GCE result differs from the corresponding canonical-ensemble result by a factor on the order of unity even in the thermodynamic limit. Thus, a widely used GCE approach does not describe correctly the critical phenomena at the phase transition for the actual systems with a fixed number of particles and yields only an asymptotics far outside the critical region.

A canonical ensemble model for a R-N black hole quantum tunneling radiation is introduced in this paper. We discover that the probability distribution function is equal to the emission rate of a spherical shell in the Parikh-Wilczek tunneling framework. Taking the generalized uncertainty principle into account, the probability distribution function corresponding to the emission shell system can be calculated with this model. As a result the concrete quantum tunneling spectrum for a R-N black hole is obtained.

We theoretically investigated the structural and thermoelectric properties of Mg2Si with Al and Sb (Na and B) as n-type (p-type) impurities. Supercell calculations involving relaxation of the atomic positions using an ab initio pseudo-potential method were performed. The formation energies, Eform, i, for the i = Mg, Si, and 4b sites, and consequently, the energetically preferred sites occupied by the impurities, were discussed. The calculated Eform, i were used to estimate the impurity-site occupancy probabilities, pi(T), based on the canonical distribution in the equilibrium state, i.e., pi(T) ∝ exp(− Eform, i/ kBT) (Boltzmann constant: kB, temperature: T), and the resultant effects on the carrier concentration. Next, an all-electron full-potential linearized augmented-plane-wave calculation was performed based on the optimized structures, and the temperature dependence of the thermoelectromotive force (the Seebeck coefficient) was evaluated using the Boltzmann transport equation. The calculated and experimental results for n-type doped systems were compared.

In general nonequilibrium steady states, directly replacing the canonical ensemble by the nonequilibrium invariant distribution yields a free energy function that is insufficient in characterizing the dynamical landscape. We address the problem by defining the free action, which is like a free energy on path space. Through a representative example, we demonstrate the conceptual and practical usefulness of the free action for quantifying the dynamics of nonequilibrium steady states, including those exhibiting phase transitions.

Our researches are based on the fact that the systems composed of polyacrylamide and montmorillonite under a kind of shear state often appear in some important practical processes like drilling well etc. The viscosity of polyacrylamide is usually the most important one among the characteristics to decide if the practical processes succeed or not. Therefore, we studied the effect of hydrated montmorillonite on the viscosities of polyacrylamide with temperature and shear rate varying under confined shear by molecular simulation method. Adopting the condition of confined shear in the research could make our simulations and the practical processes as similar as possible. First, the model of one polyacrylamide polymer chain with 20 monomers linearly linking surrounded by water molecules between two of montmorillonite layers was constructed. Then canonical ensemble (NVT) MD simulations were carried out for the built model at different temperatures and shear rates. From the gained simulation results, we calculated the polymer’s structural property-radius of gyration, which was directly related to the viscosity property of polyacrylamide polymer. It was found that the viscosity of the polyacrylamide polymer between hydrated clay layers decreased with the temperature increasing from 298 to 343 K under the condition of confined shear. The variation trend of viscosity from simulation results was also confirmed by our experiments. Besides, the viscosity of the polyacrylamide between hydrated clay layers decreased with the shear rate increasing within the range of higher shear rates.

An accurate knowledge about phase behaviors of CH4, CO2 and their binary mixture is crucial in fields of natural gas liquefaction and refrigeration applications. In this work, two all-atom force fields of TraPPE-EH and EMP2 were used for the components CH4 and CO2, respectively. Then the vapor-liquid equilibria (VLE) of CH4, CO2 and their binary system were calculated via the NVT- and NpT Gibbs Ensemble Monte Carlo Simulations. Meanwhile the traditional method using Equation of State (EoS) to correlate the VLE properties was also investigated. The EoSs considered in this work were three classic cubic RK, SRK, PR and another advanced molecular-based PC-SAFT equations. For pure components, both molecular simulations and the PC-SAFT EoS could obtain satisfactory predictions for all the saturated properties. However, the saturated liquid densities calculated by the cubic EoSs were not so good. It was also observed that the TraPPE-EH force field had a good representation for CH4 molecule, while the EMP2 force field was not enough accurate to represent CO2 molecules. For the mixture CH4 + CO2, SRK and PR showed the best predictions for the saturated pressure-component property, while good results were also obtained via molecular simulations and PC-SAFT EoS. It was suggested that special combining rules or binary interaction parameters were important to obtain enough accurate prediction of the mixed phase behavior. Compared with the cubic EoS, the PC-SAFT and molecular simulation method showed better adaptabilities for both the pure and mixture systems. Besides, the accurate molecular parameters used in the PC-SAFT and molecular simulations could bring about direct and deep understanding about the molecular characteristics.