Applications of Jarzynski's relation in lattice gauge theories

TL;DR

This paper extends Jarzynski's equality to lattice gauge theories and demonstrates its application through numerical results in specific models, offering new tools for studying non-equilibrium phenomena in quantum field theories.

Contribution

The paper introduces a novel extension of Jarzynski's relation to lattice gauge theories and explores its applications in various models and physical scenarios.

Findings

Numerical results for the $ ext{Z}_2$ gauge model in 3D.

Application to the equation of state in $ ext{SU}(2)$ Yang-Mills theory.

Discussion of potential applications in QCD and magnetic fields.

Abstract

Jarzynski's equality is a well-known result in statistical mechanics, relating free-energy differences between equilibrium ensembles with fluctuations in the work performed during non-equilibrium transformations from one ensemble to the other. In this work, an extension of this relation to lattice gauge theory will be presented, along with numerical results for the $\mathbb{Z}_2$ gauge model in three dimensions and for the equation of state in $\mathrm{SU}(2)$ Yang-Mills theory in four dimensions. Then, further applications will be discussed, in particular for the Schr\"odinger functional and for the study of QCD in strong magnetic fields.