Jarzynski Equality for Driven Quantum Field Theories

TL;DR

This paper extends the quantum Jarzynski equality to quantum field theories, specifically a time-dependent scalar phi-four theory, providing new analytical expressions and confirming the validity of fluctuation theorems at the quantum field level.

Contribution

It introduces a framework for applying the Jarzynski equality to quantum field theories, deriving explicit work distribution functions, and verifying fluctuation theorems at one-loop order.

Findings

Work distributions are proper physical observables in quantum field theory.

Jarzynski equality and Crooks theorems hold at one-loop order, independent of renormalization scale.

Pair creation processes dominate work contributions in the ultra-relativistic regime.

Abstract

The fluctuation theorems, and in particular, the Jarzynski equality, are the most important pillars of modern non-equilibrium statistical mechanics. We extend the quantum Jarzynski equality together with the Two-Time Measurement Formalism to their ultimate range of validity -- to quantum field theories. To this end, we focus on a time-dependent version of scalar phi-four. We find closed form expressions for the resulting work distribution function, and we find that they are proper physical observables of the quantum field theory. Also, we show explicitly that the Jarzynski equality and Crooks fluctuation theorems hold at one-loop order independent of the renormalization scale. As a numerical case study, we compute the work distributions for an infinitely smooth protocol in the ultra-relativistic regime. In this case, it is found that work done through processes with pair creation is the dominant contribution.