Canonical-grandcanonical ensemble in-equivalence in Fermi systems?

TL;DR

This paper investigates how fermionic condensation affects the equivalence of canonical and grandcanonical ensembles in Fermi systems, revealing that they are not equivalent at low temperatures due to corrections in chemical potential and Fermi distribution.

Contribution

It demonstrates that fermionic condensation causes ensemble in-equivalence in Fermi systems, a novel insight into statistical mechanics of such systems.

Findings

Fermionic condensation induces corrections to chemical potential.

Canonical and grandcanonical ensembles are not equivalent at low temperatures.

Ensemble in-equivalence persists even in Fermi systems with constant density of states.

Abstract

I discuss the effects of fermionic condensation in systems of constant density of states. I show that the condensation leads to a correction of the chemical potential and of the Fermi distribution in canonical Fermi systems at low temperatures. This implies that the canonical and grandcanonical ensembles are not equivalent even for Fermi systems.