The grand canonical catastrophe as an instance of condensation of fluctuations

TL;DR

This paper explains the grand canonical catastrophe in ideal Bose gases as a specific case of a broader fluctuation condensation phenomenon, linking it to experimental conditions and ensemble choices.

Contribution

It generalizes the grand canonical catastrophe as a fluctuation condensation, clarifying its nature and relation to experimental setups and statistical ensembles.

Findings

The grand canonical catastrophe is a specific instance of fluctuation condensation.

Photon condensation under grand canonical conditions exemplifies the phenomenon.

The pathological nature of the catastrophe is linked to ensemble and experimental conditions.

Abstract

The so-called grand canonical catastrophe of the density fluctuations in the ideal Bose gas is shown to be a particular instance of the much more general phenomenon of condensation of fluctuations, taking place in a large system, in or out of equilibrium, when a single degree of freedom makes a macroscopic contribution to the fluctuations of an extensive quantity. The pathological character of the "catastrophe" is demystified by emphasizing the connection between experimental conditions and statistical ensembles, as demonstrated by the recent realization of photon condensation under grand canonical conditions.