Non-standard quasiadditive integrals of motion and pressure dependence of phonon populations

TL;DR

This paper introduces a new class of quasiadditive integrals of motion that extend beyond standard variables, enabling the construction of ensembles where phonon populations depend on pressure in novel ways, differing from traditional Gibbs distributions.

Contribution

It demonstrates that any quasiadditive dynamic variable can be mapped to an integral of motion, leading to pressure-dependent phonon distributions beyond standard ensembles.

Findings

Phonon populations can depend on pressure differently than in Gibbs ensemble.

A new ensemble with pressure-dependent phonon distributions is constructed.

Extension of integrals of motion beyond standard variables is shown.

Abstract

The existing equilibrium statistical physics is based on application of standard quasiadditive integrals of motion, which include energy, momentum, rotation momentum, and number of particles. It is shown that this list is far from complete and that any quasiadditive dynamic variable can be mapped to corresponding quasiadditive integral of motion. As a result an ensemble with a given external pressure is constructed. It provides the first example of the distribution in which phonon populations depend on pressure differently than in the canonical Gibbs ensemble.