On the computation of the entropy in the microcanonical ensemble for mean-field-like systems

TL;DR

This paper compares and proves the equivalence of two recent methods for calculating entropy in the microcanonical ensemble specifically for mean-field-like systems with typical Hamiltonian structures.

Contribution

It demonstrates the equivalence of two entropy computation expressions for a class of mean-field-like systems with common Hamiltonian forms.

Findings

The two entropy expressions are mathematically equivalent.

The results apply to systems with kinetic and configurational interaction terms.

The work clarifies the theoretical foundation for entropy calculation in these systems.

Abstract

Two recently proposed expressions for the computation of the entropy in the microcanonical ensemble are compared, and their equivalence is proved. These expressions are valid for a certain class of statistical mechanics systems, that can be called mean-field-like systems. Among these, this work considers only the systems with the most usual hamiltonian structure, given by a kinetic energy term plus interaction terms depending only on the configurational coordinates.