Gauge Invariance of Equilibrium Statistical Mechanics

TL;DR

This paper demonstrates that a shifting operation on phase space acts as a gauge transformation in classical statistical mechanics, leading to exact sum rules and invariant equilibrium averages, suggesting a deeper theoretical foundation.

Contribution

It identifies a gauge invariance in classical statistical mechanics and shows how it can be used to derive exact identities and improve sampling algorithms.

Findings

Shifting operation is a gauge transformation for microstates.

Gauge invariance verified via Monte Carlo simulations.

Exact sum rules emerge from the gauge symmetry.

Abstract

We identify a recently proposed shifting operation on classical phase space as a gauge transformation for statistical mechanical microstates. The infinitesimal generators of the continuous gauge group form a non-commutative Lie algebra, which induces exact sum rules when thermally averaged. Gauge invariance with respect to finite shifting is demonstrated via Monte Carlo simulation in the transformed phase space which generates identical equilibrium averages. Our results point towards a deeper basis of statistical mechanics than previously known and they offer avenues for systematic construction of exact identities and of sampling algorithms.