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arXiv · 2210.11975

Global optimization and monotonicity in entropy production of weak drivings

Pierre Nazé
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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.

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Pierre Nazé. 2022-10-21. Global optimization and monotonicity in entropy production of weak drivings. https://doi.org/10.1103/physreve.107.024120

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