Global optimization and monotonicity in entropy production of weak drivings

TL;DR

This paper demonstrates the existence of a global optimal protocol for entropy production in finite-time, weak isothermal processes, using convexity and Euler-Lagrange techniques, confirming thermodynamic principles.

Contribution

It proves the convexity and monotonicity of entropy production functional, establishing the existence of a global optimum for weak drivings.

Findings

Existence of a global optimal protocol for entropy production.

Convexity of the entropy production functional.

Comparison of analytical and numerical optimization methods.

Abstract

Knowing if an optimal solution is local or global has always been a hard question to answer in more sophisticated situations of optimization problems. In this work, for finite-time and weak isothermal driving processes, we show the existence of a global optimal protocol for the entropy production. We prove that by showing its convexity as a functional in the derivative of the protocol. This property also proves its monotonicity in such a context, which leads to the satisfaction of the Second Law of Thermodynamics. In the end, we exemplify that the analytical technique of the Euler-Lagrange equation applied to overdamped Brownian motion delivers the global optimal protocol, by comparing it with the results of the global optimization technique of genetic programming.