Thermal momentum distribution from shifted boundary conditions

TL;DR

This paper introduces a Monte Carlo method using shifted boundary conditions to efficiently compute the thermal momentum distribution and cumulants, enabling direct measurement of thermodynamic quantities like entropy in relativistic field theories.

Contribution

It presents a novel approach linking cumulant generating functions to shifted boundary conditions, facilitating straightforward Monte Carlo evaluation of thermodynamic observables.

Findings

Successfully applied to SU(3) Yang--Mills theory

Measured entropy density at three different temperatures

Demonstrated method's effectiveness for thermodynamic calculations

Abstract

At finite temperature the distribution of the total momentum is an observable characterizing the thermal state of a field theory, and its cumulants are related to thermodynamic potentials. In a relativistic system at zero chemical potential, for instance, the thermal variance of the total momentum is a direct measure of the entropy. We relate the generating function of the cumulants to the ratio of a path integral with properly shifted boundary conditions in the compact direction over the ordinary partition function. In this form it is well suited for Monte-Carlo evaluation, and the cumulants can be extracted straightforwardly. We test the method in the SU(3) Yang--Mills theory, and obtain the entropy density at three different temperatures.