Skewed Thermodynamic Geometry and Optimal Free Energy Estimation

TL;DR

This paper introduces a geometric framework for improving free energy estimators by analyzing the influence of skewed thermodynamic geometry, with applications in drug discovery and nonequilibrium thermodynamics.

Contribution

It develops a novel geometric approach involving the supra-Stokes' tensor to optimize free energy estimation near equilibrium.

Findings

Minimum-dissipation protocols follow geodesics of the Stokes' friction tensor.

The supra-Stokes' tensor skews the geometric structure, affecting estimator bias.

Near equilibrium, the supra-Stokes' tensor dominates the leading-order bias contribution.

Abstract

Free energy differences are a central quantity of interest in physics, chemistry, and biology. We develop design principles that improve the precision and accuracy of free energy estimators, which has potential applications to screening for targeted drug discovery. Specifically, by exploiting the connection between the work statistics of time-reversed protocol pairs, we develop near-equilibrium approximations for moments of the excess work and analyze the dominant contributions to the precision and accuracy of standard nonequilibrium free-energy estimators. Within linear response, minimum-dissipation protocols follow geodesics of the Riemannian metric induced by the Stokes' friction tensor. We find the next-order contribution arises from the rank-3 supra-Stokes' tensor that skews the geometric structure such that minimum-dissipation protocols follow geodesics of a generalized cubic Finsler metric. Thus, near equilibrium the supra-Stokes' tensor determines the leading-order contribution to the bias of bidirectional free-energy estimators.