Series expansion of the excess work using nonlinear response theory

TL;DR

This paper develops a series expansion for excess work in non-equilibrium systems using nonlinear response theory, addressing large switching times and strong driving effects with a multiple-scale method.

Contribution

It introduces a novel series expansion approach for excess work in non-equilibrium thermodynamics using nonlinear response theory and a multiple-scale method.

Findings

Non-vanishing contributions for large switching times under strong driving.

The method generates a truncated series consistent with the Second Law.

Application to thermally isolated systems demonstrates the approach.

Abstract

The calculation of observable averages in non-equilibrium regimes is one of the most important problems in statistical physics. Using the Hamiltonian approach of nonlinear response theory, we obtain a series expansion of the average excess work and illustrate it with specific examples of thermally isolated systems. We report the emergence of non-vanishing contributions for large switching times when the system is subjected to strong driving. The problem is solved by using an adapted multiple-scale method to suppress these secular terms. Our paradigmatic examples show how the method is implemented generating a truncated series that obeys the Second Law of Thermodynamics.