Skewed Thermodynamic Geometry and Optimal Free Energy Estimation

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.

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Cited by in corpus (20)

• Optimal Control in Stochastic Thermodynamics
• Active matter under control: Insights from response theory
• A geometric bound on the efficiency of irreversible thermodynamic cycles
• Collective advantages in finite-time thermodynamics
• Steps minimize dissipation in rapidly driven stochastic systems
• Energy and information flows in autonomous systems
• Optimal finite-time Brownian Carnot engine
• Limited-control optimal protocols arbitrarily far from equilibrium
• Multidimensional minimum-work control of a 2D Ising model
• Performance of optimal linear-response processes in driven Brownian motion far from equilibrium
• Thermodynamic geometry of ideal quantum gases: a general framework and a geometric picture of BEC-enhanced heat engines
• Efficient two-dimensional control of barrier crossing
• Generalised linear response theory for the full quantum work statistics
• Optimal control with a strong harmonic trap
• Failure of the geometric approach prediction of excess work scaling for open and isolated quantum systems
• Scaling of Stochastic Normalizing Flows in $\mathrm{SU}(3)$ lattice gauge theory
• Time-Asymmetric Fluctuation Theorem and Efficient Free Energy Estimation
• Scaling flow-based approaches for topology sampling in $\mathrm{SU}(3)$ gauge theory
• Connections between efficient control and spontaneous transitions in an Ising model
• Optimal finite-time processes in weakly driven overdamped Brownian motion