$\mu PT$ statistical ensemble: systems with fluctuating energy, particle number, and volume

TL;DR

The paper introduces the $$ statistical ensemble, analyzing systems with fluctuating energy, particles, and volume, and discusses their statistical properties and ensemble equivalence.

Contribution

It provides a general, model-independent analysis of volume and particle number statistics within the $$ ensemble, including non-analytic points and divergent fluctuations.

Findings

Derived general features of volume and particle number statistics.

Discussed ensemble equivalence and non-analytic points of the partition function.

Analyzed quantum and classical ideal gases and a mean-field Bose gas model.

Abstract

Within the theory of statistical ensemble, the so-called $\mu PT$ ensemble describes equilibrium systems that exchange energy, particles, and volume with the surrounding. General, model-independent features of volume and particle number statistics are derived. Non-analytic points of the partition function are discussed in connection with divergent fluctuations and ensemble equivalence. Quantum and classical ideal gases, and a model of Bose gas with mean-field interactions are discussed as examples of the above considerations.