The equation of state with non-equilibrium methods

TL;DR

This paper introduces a novel out-of-equilibrium Monte Carlo method based on Jarzynski's equality to efficiently compute the equation of state of strongly-interacting matter, including SU(3) Yang-Mills theory and potential applications to QCD.

Contribution

The paper presents a new technique leveraging Jarzynski's equality for direct thermodynamic calculations in lattice gauge theories, extending to out-of-equilibrium simulations.

Findings

Computed the equation of state for SU(3) Yang-Mills theory in different phases.

Demonstrated the method's efficiency and potential for QCD thermodynamics.

Discussed generalization to theories with fermions.

Abstract

Jarzynski's equality provides an elegant and powerful tool to directly compute differences in free energy in Monte Carlo simulations and it can be readily extended to lattice gauge theories to compute a large set of physically interesting observables. In this talk we present a novel technique to determine the thermodynamics of strongly-interacting matter based on this relation, which allows for a direct and efficient determination of the pressure using out-of-equilibrium Monte Carlo simulations on the lattice. We present results for the equation of state of the $\mathrm{SU}(3)$ Yang-Mills theory in the confined and deconfined phases. Finally, we briefly discuss the generalization of this method for theories with fermions, with particular focus on the equation of state of QCD.