Foundation of Equilibrium Statistical Mechanics Based on Generalized Entropy
نویسنده
چکیده
The general mathematical formulation of the equilibrium statistical mechanics based on the generalized statistical entropy for the first and second thermodynamic potentials was given. The Tsallis and Boltzmann-Gibbs statistical entropies in the canonical and microcanonical ensembles were investigated as an example. It was shown that the statistical mechanics based on the Tsallis statistical entropy satisfies the requirements of equilibrium thermodynamics in the thermodynamic limit if the entropic index z=1/(q-1) is an extensive variable of state of the system.
منابع مشابه
Statistical mechanics of the shallow - water system with a prior potential vorticity distribution
We adapt the statistical mechanics of the shallow-water equations to the case where the flow is forced at small scales. We assume that the statistics of forcing is encoded in a prior potential vorticity distribution which replaces the specification of the Casimir constraints in the case of freely evolving flows. This determines a generalized entropy functional which is maximized by the coarse-g...
متن کاملStatistical mechanical foundations of power-law distributions
The foundations of the Boltzmann-Gibbs (BG) distributions for describing equilibrium statistical mechanics of systems are examined. Broadly, they fall into: (i) probabilistic approaches based on the principle of equal a priori probability (counting technique and method of steepest descents), law of large numbers, or the state density considerations and (ii) a variational scheme maximum entropy ...
متن کاملEquilibrium Statistical Ensembles and Structure of the Entropy Functional in Generalized Quantum Dynamics *
We review here the microcanonical and canonical ensembles constructed on an underlying generalized quantum dynamics and the algebraic properties of the conserved quantities. We discuss the structure imposed on the microcanonical entropy by the equilibrium conditions. 1 1. Introduction In this paper we review briefly the generalized quantum dynamics 1,2 constructed on a phase space of local nonc...
متن کاملThird law of thermodynamics as a key test of generalized entropies.
The laws of thermodynamics constrain the formulation of statistical mechanics at the microscopic level. The third law of thermodynamics states that the entropy must vanish at absolute zero temperature for systems with nondegenerate ground states in equilibrium. Conversely, the entropy can vanish only at absolute zero temperature. Here we ask whether or not generalized entropies satisfy this fun...
متن کاملNonlocal Bending Analysis of Bilayer Annular/Circular Nano Plates Based on First Order Shear Deformation Theory
In this paper, nonlinear bending analysis of bilayer orthotropic annular/circular graphene sheets is studied based on the nonlocal elasticity theory. The equilibrium equations are derived in terms of generalized displacements and rotations considering the first-order Shear deformation theory (FSDT). The nonlinear governing equations are solved using the differential quadrature method (DQM) whic...
متن کامل