Probability distributions in statistical ensembles with conserved charges

TL;DR

This paper derives probability distributions for charged particles in statistical ensembles with conservation laws, demonstrating the equivalence of canonical and grand canonical ensembles under proper limits at the distribution level.

Contribution

It provides a general proof of ensemble equivalence at the probability distribution level for systems with conserved charges.

Findings

Canonical and grand canonical ensembles are equivalent when limits are properly taken.

The equivalence holds at the most general probability distribution level.

Derived explicit probability distributions for charged particle numbers.

Abstract

The probability distributions for charged particle numbers and their densities are derived in statistical ensembles with conservation laws. It is shown that if this limit is properly taken then the canonical and grand canonical ensembles are equivalent. This equivalence is proven on the most general, probability distribution level.