Thermodynamic metrics and optimal paths

TL;DR

This paper introduces a thermodynamic metric based on a friction tensor that helps identify optimal paths for finite-time transformations, minimizing dissipation in molecular-scale machines operating away from equilibrium.

Contribution

It derives a new thermodynamic metric tensor that defines a Riemannian manifold on thermodynamic states, enabling the determination of optimal protocols in nonequilibrium thermodynamics.

Findings

The metric controls dissipation in finite-time thermodynamic processes.

Optimal protocols exhibit desirable properties within the linear-response regime.

Application to a simple model demonstrates practical utility.

Abstract

A fundamental problem in modern thermodynamics is how a molecular-scale machine performs useful work, while operating away from thermal equilibrium without excessive dissipation. To this end, we derive a friction tensor that induces a Riemannian manifold on the space of thermodynamic states. Within the linear-response regime, this metric structure controls the dissipation of finite-time transformations, and bestows optimal protocols with many useful properties. We discuss the connection to the existing thermodynamic length formalism, and demonstrate the utility of this metric by solving for optimal control parameter protocols in a simple nonequilibrium model.