A unified, geometric framework for nonequilibrium protocol optimization

TL;DR

This paper introduces a unified geometric framework for optimizing nonequilibrium control protocols to minimize dissipation in thermodynamic systems, applicable to nanoscale systems and beyond linear response.

Contribution

It develops a theoretical and computational approach linking thermodynamic metrics with optimal transport, providing a new unified perspective on nonequilibrium protocol optimization.

Findings

Protocols optimized via the framework reduce dissipation in model systems.

The thermodynamic metric can be derived from the same objective as optimal transport.

The approach is robust beyond linear response regimes.

Abstract

Controlling thermodynamic cycles to minimize the dissipated heat is a longstanding goal in thermodynamics, and more recently, a central challenge in stochastic thermodynamics for nanoscale systems. Here, we introduce a theoretical and computational framework for optimizing nonequilibrium control protocols that can transform a system between two distributions in a minimally dissipative fashion. These protocols optimally transport a system along paths through the space of probability distributions that minimize the dissipative cost of a transformation. Furthermore, we show that the thermodynamic metric -- determined via a linear response approach -- can be directly derived from the same objective function that is optimized in the optimal transport problem, thus providing a unified perspective on thermodynamic geometries. We investigate this unified geometric framework in two model systems and observe that our procedure for optimizing control protocols is robust beyond linear response.