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Constraint of a fixed total number of particles yields a correlation between the fluctuation of particles in different states in the canonical ensemble. Here we show that, below the temperature of Bose–Einstein condensation (BEC), the correlation part of the entropy of an ideal Bose gas is cancelled by the ground-state contribution. Thus, in the BEC region, the thermodynamic properties of the gas in the canonical ensemble can be described accurately in a simplified model which excludes the ground state and assumes no correlation between excited levels.

It is very important to determine the phase transition temperature, such as the water/ice coexistence temperature in various water models, via molecular simulations. We show that a single individual direct simulation is sufficient to get the temperature with high accuracy and small computational cost based on the generalized canonical ensemble (GCE). Lennard–Jones fluids, the atomic water models, such as TIP4P/2005, TIP4P/ICE, and the mW water models are applied to illustrate the method. We start from the coexistent system of the two phases with a plane interface, then equilibrate the system under the GCE, which can stabilize the coexistence of the phases, to directly derive the phase transition temperature without sensitive dependence on the applied parameters of the GCE and the size of the simulation systems. The obtained result is in excellent agreement with that in literatures. These features make the GCE approach in determining the phase transition temperature of systems be robust, easy to use, and particularly good at working on computationally expensive systems. [ABSTRACT FROM AUTHOR]

Close to equilibrium, the excess heat governs the static fluctuations. We study the heat capacity in that McLennan regime, i.e. in linear order around equilibrium, using an expression in terms of the average energy that extends the equilibrium formula in the canonical ensemble. It is derivable from an entropy and it always vanishes at zero temperature. Any violation of an extended Third Law is therefore a nonlinear effect. [ABSTRACT FROM AUTHOR]

Constraint of a fixed total number of particles yields a correlation between the fluctuation of particles in different states in the canonical ensemble. Here we show that, below the temperature of Bose-Einstein condensation (BEC), the correlation part of the entropy of an ideal Bose gas is cancelled by the ground-state contribution. Thus, in the BEC region, the thermodynamic properties of the gas in the canonical ensemble can be described accurately in a simplified model which excludes the ground state and assumes no correlation between excited levels. [ABSTRACT FROM AUTHOR]

A canonical ensemble model for the black hole quantum tunneling radiation is introduced. With this model the probability distribution function corresponding to the emission shell is calculated. Comparing with this function, we investigate the statistical significance of the quantum tunneling radiation spectrum of black holes. Moreover, by calculating the entropy of the emission shell, a discussion about the mechanism of information flowing out from the black hole is given out. [ABSTRACT FROM AUTHOR]

L -ensembles are a class of determinantal point processes which can be viewed as a statistical mechanical systems in the grand canonical ensemble. Circulant L -ensembles are the subclass which are locally translationally invariant and furthermore subject to periodic boundary conditions. Existing theory can very simply be specialised to this setting, allowing for the derivation of formulas for the system pressure, and the correlation kernel, in the thermodynamic limit. For a one-dimensional domain, this is possible when the circulant matrix is both real symmetric, or complex Hermitian. The special case of the former having a Gaussian functional form for the entries is shown to correspond to free fermions at finite temperature, and be generalisable to higher dimensions. A special case of the latter is shown to be the statistical mechanical model introduced by Gaudin to interpolate between Poisson and unitary symmetry statistics in random matrix theory. It is shown in all cases that the compressibility sum rule for the two-point correlation is obeyed, and the small and large distance asymptotics of the latter are considered. Also, a conjecture relating the asymptotic form of the hole probability to the pressure is verified. [ABSTRACT FROM AUTHOR]

We give a descriptive review of the fermionic basis approach to the theory of correlation functions of the XXZ quantum spin chain. The emphasis is on explicit formulae for short-range correlation functions which will be presented in a way that allows for their direct implementation on a computer. Within the fermionic basis approach a huge class of stationary reduced density matrices, compatible with the integrable structure of the model, assumes a factorized form. This means that all expectation values of local operators and all two-point functions, in particular, can be represented as multivariate polynomials in only two functions ρ and ω and their derivatives with coefficients that are rational in the deformation parameter q of the model. These coefficients are of 'algebraic origin'. They do not depend on the choice of the density matrix, which only impacts the form of ρ and ω. As an example we work out in detail the case of the grand canonical ensemble at temperature T and magnetic field h for q in the critical regime. We compare our exact results for the fourth-neighbour two-point functions with asymptotic formulae for h, T = 0 and for finite h and T. [ABSTRACT FROM AUTHOR]

The asymptotic equivalence of canonical and microcanonical ensembles is a central concept in statistical physics, with important consequences for both theoretical research and practical applications. However, this property breaks down under certain circumstances. The most studied violation of ensemble equivalence requires phase transitions, in which case it has a ‘restricted’ (i.e. confined to a certain region in parameter space) but ‘strong’ (i.e. characterized by a difference between the entropies of the two ensembles that is of the same order as the entropies themselves) form. However, recent research on networks has shown that the presence of an extensive number of local constraints can lead to ensemble nonequivalence (EN) even in the absence of phase transitions. This occurs in a ‘weak’ (i.e. leading to a subleading entropy difference) but remarkably ‘unrestricted’ (i.e. valid in the entire parameter space) form. Here we look for more general manifestations of EN in arbitrary ensembles of matrices with given margins. These models have widespread applications in the study of spatially heterogeneous and/or temporally nonstationary systems, with consequences for the analysis of multivariate financial and neural time-series, multi-platform social activity, gene expression profiles and other big data. We confirm that EN appears in ‘unrestricted’ form throughout the entire parameter space due to the extensivity of local constraints. Surprisingly, at the same time it can also exhibit the ‘strong’ form. This novel, simultaneously ‘strong and unrestricted’ form of nonequivalence is very robust and imposes a principled choice of the ensemble. We calculate the proper mathematical quantities to be used in real-world applications. [ABSTRACT FROM AUTHOR]

Molecular or condensed matter systems are often well approximated by hybrid quantum-classical models: the electrons retain their quantum character, whereas the ions are considered to be classical particles. We discuss various alternative approaches for the computation of equilibrium (canonical) ensemble averages for observables of these hybrid quantum-classical systems through the use of molecular dynamics (MD)-i.e. by performing dynamics in the presence of a thermostat and computing time-averages over the trajectories. Often, in classical or ab initio MD, the temperature of the electrons is ignored and they are assumed to remain at the instantaneous ground state given by each ionic configuration during the evolution. Here, however, we discuss the general case that considers both classical and quantum subsystems at finite temperature canonical equilibrium. Inspired by a recent formal derivation for the canonical ensemble for quantum classical hybrids, we discuss previous approaches found in the literature, and provide some new formulas. [ABSTRACT FROM AUTHOR]

Dark solitons are common topological excitations in a wide array of nonlinear waves. The dark soliton excitation energy is crucial for exploring dark soliton dynamics and is necessarily calculated in a renormalized form due to its existence on a finite background. Despite its tremendous importance and success, the renormalized energy form was at first only suggested with no detailed derivation, and was then "derived" in the grand canonical ensemble. We revisit this fundamental problem and provide an alternative and intuitive derivation of the energy form from the fundamental field energy by utilizing a limiting procedure that conserves number of particles. Our derivation yields the same result, thus putting the dark soliton energy form on a solid basis. [ABSTRACT FROM AUTHOR]

Quantum fluctuation consequences have significant role in high-energy physics. These fluctuation often regarded as a correction of the infrared (IR) limit. Such correction contribute to the high-energy limit of thermodynamical quantities and the stability conditions of black holes. In this work, we analyze the thermal stability of black holes in the presence of thermal fluctuations. We consider AdS black hole in Born–Infeld massive gravity with non-abelian hair and the charged AdS black hole with a global monopole. We develop many thermodynamical quantities such as entropy, temperature, pressure, heat capacity of a system at constant volume and pressure, ratio between the heat capacities at constant pressure and volume, Gibbs free energy and Helmholtz free energy for both black holes. The critical behavior and phase transitions of black holes are also presented. We also observe the local and global stability of black holes in the grand canonical ensemble and canonical ensemble for the specific values of different parameters, such as, symmetry breaking parameter η, massive parameter m and non-abelian hair ν. [ABSTRACT FROM AUTHOR]

We develop a novel method to analyze the excluded volume of the multicomponent mixtures of classical hard spheres in the grand canonical ensemble. The method is based on the Laplace–Fourier transform technique and allows one to account for the fluctuations of the particle number density for the induced surface and curvature tensions equation of state. As a result one can go beyond the Van der Waals (VdW) approximation by obtaining the suppression of the induced surface and curvature tensions coefficients at moderate and high packing fractions. In contrast to the standard induced surface and curvature tensions equation of state the suppression of these coefficients is not the exponential, but a power-like one. The obtained alternative equation of state is further generalized to account for higher virial coefficients. This result is straightforwardly generalized to the case of quantum statistics. [ABSTRACT FROM AUTHOR]

The irreversible adsorption of polyatomic (or k-mers) on linear chains is related to phenomena such as the adsorption of colloids, long molecules, and proteins on solid substrates. This process generates jammed or blocked final states. In the case of k = 2, the binomial coefficient computes the number of final states. By the canonical ensemble, the Boltzmann–Gibbs–Shannon entropy function is obtained by using Stirling's approximation, and its equilibrium density ρeq,2 is its maximum at the thermodynamic limit with value ρeq,2 ≈ 0.822 991 17. Moreover, since at the same energy we have several possible configurations, we obtain the state probability density. Maximizing the entropy, it converges to a Gaussian distribution as L → ∞. In this article, we generalize this analysis to k > 2 to maximize the entropy and to get the equilibrium densities ρeq,k. We first develop a complete combinatorial analysis to get the generalized recurrence formula (GRF) for counting all blocked configuration states on a chain of length L with fixed k, which corresponds to a generalized truncated Fibonacci sequence. The configuration states for allocating N k-mers is related with the general binomial coefficient. Since Stirling's approximation cannot be used for GRF, we numerically compute the state probability density and approximate ρeq,k and σeq,k for large k-mers with high precision for k-mers up to k = 1, 000, 000. We highlight that ρeq,k decreases from k = 2, ..., 8 reaching a minimum at k = 9 and then increases with an asymptotic value ρeq,∞ = 0.9285685. We compared with jamming densities obtained by RSA and at k ≈ 16, both curves intersect and ergodicity is not broken since ρjam,k ≈ ρeq,k. In the case of , it grows similarly with asymptotic value. Since the similar behavior for large values, we found the limit relationship as L → ∞ for any k. Finally, as k → ∞, we get the Gaussian distribution for the continuous blocked irreversible adsorption or equivalent to the irreversible blocked car parking problem. [ABSTRACT FROM AUTHOR]

We study the bond percolation problem under the constraint that the total number of occupied bonds is fixed, so that the canonical ensemble applies. We show via an analytical approach that at criticality, the constraint can induce new finite-size corrections with exponent ycan = 2yt - d both in energy-like and magnetic quantities, where yt = 1/? is the thermal renormalization exponent and d is the spatial dimension. Furthermore, we find that while most of the universal parameters remain unchanged, some universal amplitudes, like the excess cluster number, can be modified and become non-universal. We confirm these predictions by extensiveMonte Carlo simulations of the two-dimensional percolation problem which has ycan = -1/2. [ABSTRACT FROM AUTHOR]

The dynamics of zero-range processes on complex networks is expected to be influenced by the topological structure of underlying networks. A real space complete condensation phase transition in the stationary state may occur. We study the finite density effects of the condensation transition in both the stationary and dynamical zero-range processes on scale-free networks. By means of grand canonical ensemble method, we predict analytically the scaling laws of the average occupation number with respect to the finite density for the steady state. We further explore the relaxation dynamics of the condensation phase transition. By applying the hierarchical evolution and scaling ansatz, a scaling law for the relaxation dynamics is predicted. Monte Carlo simulations are performed and the predicted density scaling laws are nicely validated. [ABSTRACT FROM AUTHOR]

The structure factor for electric field correlations in the two dimensional Coulomb fluid is simulated and compared to theories of the dielectric function. Singular changes in the structure factor occur at the Berezinskiiâ€"Kosterlitzâ€"Thouless insulator to conductor transition, as well as at a higher temperature correlation transition between a poor electrolyte and perturbed Debyeâ€"HĂĽckel fluid. Structure factors are found to differ in the canonical and grand canonical ensembles, with the poor electrolyte showing full ensemble inequivalence. We identify mechanisms of ‘underscreening’ and ‘pinch point’ scattering that are relevant to experiments on ionic liquids and artificial spin ice respectively. [ABSTRACT FROM AUTHOR]