Temperature and equipartition in discrete systems

TL;DR

This paper extends the conjugate variables theorem to discrete systems, deriving new thermodynamic identities that connect temperature with measurable observables in the canonical ensemble.

Contribution

It introduces a generalized form of the equipartition theorem for discrete variables, expanding its applicability beyond continuous systems.

Findings

Derived novel thermodynamic identities for discrete systems

Extended the conjugate variables theorem to discrete variables

Connected temperature with measurable observables in the canonical ensemble

Abstract

The generalized equipartition theorem known as the conjugate variables theorem (Phys. Rev. E 86, 051136 [2012]), originally obtained in the context of statistical inference of continuous random variables, is extended in this work to the case of discrete variables. Using this new set of theorems we derive novel thermodynamic identities for the canonical ensemble connecting temperature with measurable observables.