{
  "id": "2404.01286",
  "version": "v2",
  "published": "2024-04-01T17:56:28.000Z",
  "updated": "2024-04-02T17:27:36.000Z",
  "title": "Beyond Linear Response: Equivalence between Thermodynamic Geometry and Optimal Transport",
  "authors": [
    "Adrianne Zhong",
    "Michael R. DeWeese"
  ],
  "comment": "Typos corrected. 7 pages, 2 figures main text; 7 pages, 2 figures SI. Comments welcome",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "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.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2024-04-02T17:27:36.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "thermodynamic geometry",
      "equivalence",
      "obtaining optimal protocols past",
      "parameteric harmonic potentials",
      "linear response regime"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}