Geometrical aspects of a generalized statistical mechanics

TL;DR

This paper explores the geometric properties of generalized entropy measures in statistical mechanics, focusing on phase transitions, critical behavior, and thermodynamic stability through a geometric framework.

Contribution

It introduces a geometric approach to analyze generalized entropy forms and their relation to phase transitions and stability in thermodynamic systems.

Findings

Geometric characterization of phase transitions.

Insights into thermodynamic stability conditions.

Application of generalized entropy to critical phenomena.

Abstract

We discuss here the use of generalized forms of entropy, taken as information measures, to characterize phase transitions and critical behavior in thermodynamic systems. Our study is based on geometric considerations pertaining to the space of parameters that describe statistical mechanics models. The thermodynamic stability of the system is the focus of attention in this geometric context.