Measuring thermodynamic length

TL;DR

This paper explores the concept of thermodynamic length, its theoretical properties, and how it can be measured in small systems via computer simulations, revealing connections to established statistical metrics.

Contribution

It introduces a method to define and measure thermodynamic length in small systems using computer simulations, linking it to Bennett's acceptance ratio method.

Findings

Thermodynamic length bounds dissipation in finite-time transformations.

Bennett's acceptance ratio method also measures thermodynamic length.

The paper provides a practical approach for measuring thermodynamic length in simulations.

Abstract

Thermodynamic length is a metric distance between equilibrium thermodynamic states. Among other interesting properties, this metric asymptotically bounds the dissipation induced by a finite time transformation of a thermodynamic system. It is also connected to the Jensen-Shannon divergence, Fisher information and Rao's entropy differential metric. Therefore, thermodynamic length is of central interest in understanding matter out-of-equilibrium. In this paper, we will consider how to define thermodynamic length for a small system described by equilibrium statistical mechanics and how to measure thermodynamic length within a computer simulation. Surprisingly, Bennett's classic acceptance ratio method for measuring free energy differences also measures thermodynamic length.