Related papers: On the entropy minimization problem in Statistical…
Statistical entropies of a general relativistic ideal gas obeying Maxwell-Boltzmann, Bose-Einstein and Fermi-Dirac statistics are calculated in a general axisymmetry space-time of arbitrary dimension. This general formation can be used to…
The exact Maxwell-Boltzmann (MB), Bose-Einstein (BE) and Fermi-Dirac (FD) entropies and probabilistic distributions are derived by the combinatorial method of Boltzmann, without Stirling's approximation. The new entropy measures are…
The violation of the Pauli principle has been surmised in several models of the Fractional Exclusion Statistics and successfully applied to several quantum systems. In this paper, a classical alternative of the exclusion statistics is…
The montecarlo method, which is quite commonly used to solve maximum entropy problems in statistical physics, can actually be used to solve inverse problems in a much wider context. The probability distribution which maximizes entropy can…
We derive Bose-Einstein statistics and Fermi-Dirac statistics by Principle of Maximum Entropy applied to two families of entropy functions different from the Boltzmann-Gibbs-Shannon entropy. These entropy functions are identified with…
We show that the principle of maximum entropy, a variational method appearing in statistical inference, statistical physics, and the analysis of stochastic dynamical systems, admits a geometric description from gauge theory. Using the…
Based on a characterization of the optimality of a feasible solution of a convex entropy minimization problem, one shows that the feasible solutions obtained using formally the Lagrange multipliers method are optimal.
We consider the problem of minimizing a generalized relative entropy, with respect to a reference diffusion law, over the set of path-measures with fully prescribed marginal distributions. When dealing with the actual relative entropy,…
This study investigates the steady Boltzmann equation in one spatial variable for a polyatomic single-component gas in a half-space. Inflow boundary conditions are assumed at the half-space boundary, where particles entering the half-space…
We propose a method to derive the stationary size distributions of a system, and the degree distributions of networks, using maximisation of the Gibbs-Shannon entropy. We apply this to a preferential attachment-type algorithm for systems of…
The thermodynamic maximum principle for the Boltzmann-Gibbs-Shannon (BGS) entropy is reconsidered by combining elements from group and measure theory. Our analysis starts by noting that the BGS entropy is a special case of relative entropy.…
In this paper, using of the rigorous statement and rigorous proof the Maxwell distribution as an example, we establish estimates of the distribution depending on the parameter $N$, the number of particles. Further, we consider the problem…
In ordinary statistical mechanics the Boltzmann-Shannon entropy is related to the Maxwell-Bolzmann distribution $p_i$ by means of a twofold link. The first link is differential and is offered by the Jaynes Maximum Entropy Principle. The…
The most rigorous physical description of non-equilibrium gas dynamics is rooted in the numerical solution of the Boltzmann equation. Yet, the large number of degrees of freedom and the wide range of both spatial and temporal scales render…
The approach of an ideal gas to equilibrium is simulated through a generalization of the Ehrenfest ball-and-box model. In the present model, the interior of each box is discretized, {\it i.e.}, balls/particles live in cells whose occupation…
In this study we apply the maximum entropy principle to derive the properly scaled velocity distribution function of Boltzmann equations for mixtures, which leads to a non-isothermal Maxwell-Stefan diffusion model. We also analyze the…
We consider a system composed of a fixed number of particles with total energy smaller or equal to some prescribed value. The particles are non-interacting, indistinguishable and distributed over fixed number of energy levels. The energy…
The paper analyzes the entropy of a system composed by non-interacting and indistinguishable particles whose quantum state numbers are modelled as independent and identically distributed classical random variables. The crucial observation…
Generalized Bose-Einstein (BE) and Fermi-Dirac (FD) distributions in nonextensive quantum statistics have been discussed by the maximum-entropy method (MEM) with the optimum Lagrange multiplier based on the exact integral representation…
We propose a new formulation of the fluctuating lattice Boltzmann equation that is consistent with both equilibrium statististical mechanics and fluctuating hydrodynamics. The formalism is based on a generalized lattice-gas model, with each…