Beyond Linear Response: Equivalence between Thermodynamic Geometry and Optimal Transport

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• Adrianne Zhong, UC Berkeley
• Tuesday 05 November 2024, 13:00-14:00
• Center for Mathematical Sciences, Lecture room MR4.

If you have a question about this talk, please contact Balázs Németh.

A fundamental result of thermodynamic geometry is that the optimal, minimal-work protocol that drives a nonequilibrium system between two thermodynamic states in the slow-driving limit is given by a geodesic of the friction tensor, a Riemannian metric defined on control space. For overdamped dynamics in arbitrary dimensions, we demonstrate that thermodynamic geometry is equivalent to 𝐿2 optimal transport geometry defined on the space of equilibrium distributions corresponding to the control parameters. We show that obtaining optimal protocols past the slow-driving or linear response regime is computationally tractable as the sum of a friction tensor geodesic and a counterdiabatic term related to the Fisher information metric. These geodesic-counterdiabatic optimal protocols are exact for parametric harmonic potentials, reproduce the surprising nonmonotonic behavior recently discovered in linearly biased double well optimal protocols, and explain the ubiquitous discontinuous jumps observed at the beginning and end times.

This talk is part of the DAMTP Statistical Physics and Soft Matter Seminar series.

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• Center for Mathematical Sciences, Lecture room MR4
• DAMTP Statistical Physics and Soft Matter Seminar
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