Inherent correlations between thermodynamics and statistic physics in extensive and nonextensive systems

TL;DR

This paper explores the fundamental links between thermodynamics and statistical mechanics in both extensive and nonextensive systems, revealing their equivalence through the MaxEnt approach and deriving related probability distributions.

Contribution

It introduces a general entropy expression unifying extensive and nonextensive systems and demonstrates their thermodynamic-statistical relations using the MaxEnt method.

Findings

Equivalence of thermodynamic laws and MaxEnt in isothermal processes

Derived probability distributions for nonextensive and extensive systems

Calculated generalized forces for specific systems

Abstract

With the help of a general expression of the entropies in extensive and nonextensive systems, some important relations between thermodynamics and statistical mechanics are revealed through the views of thermodynamics and statistic physics. These relations are proved through the MaxEnt approach once again. It is found that for a reversible isothermal process, the information contained in the first and second laws of thermodynamics and the MaxEnt approach is equivalent. Moreover, these relations are used to derive the probability distribution functions in nonextensive and extensive statistics and calculate the generalized forces of some interesting systems. The results obtained are of universal significance.