Geometrical aspects and connections of the energy-temperature fluctuation relation

TL;DR

This paper explores a generalized fluctuation relation linking energy fluctuations and heat capacity, highlighting its implications for negative heat capacities and connections to geometric formulations in statistical mechanics.

Contribution

It presents a comprehensive overview of the implications and connections of a generalized fluctuation relation with geometric and computational methods in statistical mechanics.

Findings

Extension of canonical Monte Carlo methods

Geometric formulation of fluctuation theory

Relevance of geometric extension of Gibbs ensemble

Abstract

Recently, we have derived a generalization of the known canonical fluctuation relation $k_{B}C=\beta^{2}< \delta U^{2} >$ between heat capacity $C$ and energy fluctuations, which can account for the existence of macrostates with negative heat capacities $C<0$. In this work, we presented a panoramic overview of direct implications and connections of this fluctuation theorem with other developments of statistical mechanics, such as the extension of canonical Monte Carlo methods, the geometric formulations of fluctuation theory and the relevance of a geometric extension of the Gibbs canonical ensemble that has been recently proposed in the literature.