Ensemble equivalence for non-Bolztmannian distributions

TL;DR

This paper explores the use of generalized canonical distributions beyond the traditional Boltzmann factor to simplify the calculation of equilibrium properties in physical systems, demonstrating equivalence with standard methods.

Contribution

It introduces a framework for using alternative factors in canonical distributions and proves their equivalence to traditional distributions in certain cases.

Findings

Generalized distributions can simplify equilibrium calculations.

Equivalence between canonical and generalized distributions is established.

Application to the long-range Ising model demonstrates the method's effectiveness.

Abstract

We discuss the possibility of using generalized canonical distributions, i.e. using other factors than $\exp(-\beta E)$, in order to compute the equilibrium properties of physical systems. It will be show that some other choices can, in certain cases, lead to a simpler calculation of those properties. The corresponding equivalence between the canonical and the generalized canonical distributions is derived using well-known principles of Statistical Mechanics and we exemplify the method by deriving in a simple way the equilibrium properties of the long--range Ising model.