Geometrical aspects and connections of the energy-temperature fluctuation relation

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.

arXiv commentVersion accepted for publication in J. Phys. A: Math and Theo

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Cited by in corpus (6)

• Equilibrium fluctuation theorems compatible with anomalous response
• Extending canonical Monte Carlo methods
• Improving the efficiency of Monte Carlo simulations of systems that undergo temperature-driven phase transitions
• Extended canonical Monte Carlo methods: Improving accuracy of microcanonical calculations using a re-weighting technique
• Extending canonical Monte Carlo methods II
• Understanding critical behavior in the framework of the extended equilibrium fluctuation theorem