Beyond Linear Response: Equivalence between Thermodynamic Geometry and Optimal Transport
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866916448982532096 |
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| author | Zhong, Adrianne DeWeese, Michael R. |
| author_facet | Zhong, Adrianne DeWeese, Michael R. |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2404_01286 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Beyond Linear Response: Equivalence between Thermodynamic Geometry and Optimal Transport Zhong, Adrianne DeWeese, Michael R. Statistical Mechanics 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. |
| title | Beyond Linear Response: Equivalence between Thermodynamic Geometry and Optimal Transport |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2404.01286 |