Thermodynamic optimization equalities in weakly driven processes

TL;DR

This paper derives thermodynamic equalities for weakly driven open systems, providing a new way to verify optimality conditions and improve optimization methods like genetic programming.

Contribution

It introduces novel equalities from the Euler-Lagrange equation that link thermodynamic optimization to path-independence of work and heat.

Findings

Equalities serve as convergence criteria in optimization.

Results extend to variances via fluctuation-dissipation relations.

Equalities are applicable to classical open systems.

Abstract

Equalities are generally more suitable for experimental verification than inequalities. In this work, I derive valid equalities from the Euler-Lagrange equation for the optimization of macroscopic thermodynamic averages in weakly driven classical open systems. These equalities show that optimization occurs when work and heat become path-independent. I illustrate their applicability by employing them as a convergence criterion in the global optimization technique of genetic programming. Moreover, due to fluctuation-dissipation relations for internal energy, work, and heat, analogous results hold for their variances.