Far-from-Equilibrium Measurements of Thermodynamic Length

TL;DR

This paper demonstrates how to measure thermodynamic length in far-from-equilibrium single molecule experiments using work fluctuation relations and Fisher information, enabling new insights into microscopic thermodynamics.

Contribution

It introduces a method to measure thermodynamic length far from equilibrium by relating it to fluctuations and extending Bennett's method for single molecule experiments.

Findings

Thermodynamic length can be measured in out-of-equilibrium conditions.

Fisher information is essential for defining thermodynamic length microscopically.

The method extends Bennett's approach to determine free energy and thermodynamic length.

Abstract

Thermodynamic length is a path function that generalizes the notion of length to the surface of thermodynamic states. Here, we show how to measure thermodynamic length in far-from-equilibrium single molecule experiments using the work fluctuation relations. For these microscopic systems, it proves necessary to define the thermodynamic length in terms of the Fisher information. Consequently, the thermodynamic length can be directly related to the magnitude of fluctuations about equilibrium. The work fluctuation relations link the work and the free energy change during an external perturbation on a system. We use this result to determine equilibrium averages at intermediate points of the protocol in which the system is out-of-equilibrium. This allows us to extend Bennett's method to determine the potential of mean force, as well as the thermodynamic length, in single molecule experiments.