Geometric variations of the Boltzmann entropy

TL;DR

This paper analyzes how the Boltzmann entropy varies infinitesimally with energy in finite systems, providing insights into the stability of these variations and their geometric interpretation.

Contribution

It introduces a geometric approach to the variations of Boltzmann entropy, focusing on first and second order infinitesimal changes with respect to energy.

Findings

First and second order variations of Boltzmann entropy are explicitly calculated.

The stability of the entropy variations is discussed through the second variation.

The geometric interpretation of entropy variations offers new insights into thermodynamic stability.

Abstract

We perform a calculation of the first and second order infinitesimal variations, with respect to energy, of the Boltzmann entropy of constant energy hypersurfaces of a system with a finite number of degrees of freedom. We comment on the stability interpretation of the second variation in this framework.