Statistical ensemble equivalence problem

TL;DR

This paper critically examines the equivalence of statistical ensembles, revealing that certain semi-intensive variables retain memory of the underlying ensemble even in the thermodynamic limit, highlighting a universal property.

Contribution

It demonstrates that semi-intensive variables preserve ensemble-specific information, challenging the assumption of ensemble equivalence in statistical physics.

Findings

Semi-intensive variables retain ensemble memory in the thermodynamic limit

Ensemble equivalence does not hold for all physical observables

The property is universal, observed even in simple classical ensembles

Abstract

A problem of the equivalence of statistical ensembles is critically analyzed. It is shown, that although different probability distributions of statistical physics have the same behavior in the thermodynamic limit, there are physical observables -- semi-intensive variables -- which keep memory of the underlying ensembles. This property is an universal one and can be observed even in the simplest case of the grand canonical and canonical ensembles of the classical statistical physics.