Legendre transforms of the fundamental thermodynamic relation and statistical ensembles

TL;DR

This paper demonstrates how Legendre transforms of the fundamental thermodynamic relation can be employed to systematically derive various statistical ensembles, providing a unified theoretical framework.

Contribution

It introduces a method to generate different statistical ensembles from thermodynamics using Legendre transforms, clarifying their interrelations.

Findings

Unified framework for statistical ensembles via Legendre transforms

Derivation of ensembles from thermodynamic relations

Enhanced understanding of ensemble interconnections

Abstract

We show how the Legendre transforms of the fundamental thermodynamic relation can be used to introduce different statistical ensembles.