Current browse context:
cond-mat.stat-mech
Change to browse by:
References & Citations
Condensed Matter > Statistical Mechanics
Title: Beyond Linear Response: Equivalence between Thermodynamic Geometry and Optimal Transport
(Submitted on 1 Apr 2024 (v1), last revised 26 Apr 2024 (this version, v4))
Abstract: 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 $L^2$ 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 parameteric harmonic potentials, reproduce the surprising non-monotonic behavior recently discovered in linearly-biased double well optimal protocols, and explain the ubiquitous discontinuous jumps observed at the beginning and end times.
Submission history
From: Adrianne Zhong [view email][v1] Mon, 1 Apr 2024 17:56:28 GMT (816kb,D)
[v2] Tue, 2 Apr 2024 17:27:36 GMT (812kb,D)
[v3] Thu, 25 Apr 2024 02:31:46 GMT (808kb,D)
[v4] Fri, 26 Apr 2024 01:03:07 GMT (811kb,D)
Link back to: arXiv, form interface, contact.