Generalized Second Law and optimal protocols for nonequilibrium systems

TL;DR

This paper extends the Maximum Work Theorem to nonequilibrium initial states, analyzes trajectory violations, and identifies optimal protocols that minimize entropy change, revealing that optimality does not always correlate with maximum violations.

Contribution

It introduces a generalized theorem for nonequilibrium systems, studies violation fractions in simple models, and finds optimal protocols that minimize entropy change.

Findings

Violation fraction does not always increase with protocol optimization.

Optimal protocols can minimize entropy change without maximizing violations.

The generalized theorem applies to systems starting out of equilibrium.

Abstract

A generalized version of the Maximum Work Theorem is valid when the system is initially not at thermal equilibrium. In this work, we initially study the fraction of trajectories that violate this generalized theorem for a two simple systems: a particle in a harmonic trap (i) whose centre is dragged with some protocol, and (ii) whose stiffness constant changes as a function of time. We also find the optimal protocol that minimizes the average change in total entropy. To our surprise, we find that optimization of protocol does not necessarily entail maximum violation fraction.