Geometrical aspects of entropy production in stochastic thermodynamics based on Wasserstein distance
We study a relationship between optimal transport theory and stochastic thermodynamics for the Fokker-Planck equation. We show that the lower bound on the entropy production is the action measured by the path length of the L^{2}-Wasserstein distance. Because the L^{2}-Wasserstein distance is a geome...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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American Physical Society
2021-11-01
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| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/PhysRevResearch.3.043093 |
| _version_ | 1797210890974527488 |
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| author | Muka Nakazato Sosuke Ito |
| author_facet | Muka Nakazato Sosuke Ito |
| author_sort | Muka Nakazato |
| collection | DOAJ |
| description | We study a relationship between optimal transport theory and stochastic thermodynamics for the Fokker-Planck equation. We show that the lower bound on the entropy production is the action measured by the path length of the L^{2}-Wasserstein distance. Because the L^{2}-Wasserstein distance is a geometric measure of optimal transport theory, our result implies a geometric interpretation of the entropy production. Based on this interpretation, we obtain a thermodynamic trade-off relation between transition time and the entropy production. This thermodynamic trade-off relation is regarded as a thermodynamic speed limit which gives a tighter bound of the entropy production. We also discuss stochastic thermodynamics for the subsystem and derive a lower bound on the partial entropy production as a generalization of the second law of information thermodynamics. Our formalism also provides a geometric picture of the optimal protocol to minimize the entropy production. We illustrate these results by the optimal stochastic heat engine and show a geometrical bound of the efficiency. |
| first_indexed | 2024-04-24T10:17:47Z |
| format | Article |
| id | doaj.art-dbc735c4971248b499a2067a07cc0ac3 |
| institution | Directory Open Access Journal |
| issn | 2643-1564 |
| language | English |
| last_indexed | 2024-04-24T10:17:47Z |
| publishDate | 2021-11-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Research |
| spelling | doaj.art-dbc735c4971248b499a2067a07cc0ac32024-04-12T17:15:22ZengAmerican Physical SocietyPhysical Review Research2643-15642021-11-013404309310.1103/PhysRevResearch.3.043093Geometrical aspects of entropy production in stochastic thermodynamics based on Wasserstein distanceMuka NakazatoSosuke ItoWe study a relationship between optimal transport theory and stochastic thermodynamics for the Fokker-Planck equation. We show that the lower bound on the entropy production is the action measured by the path length of the L^{2}-Wasserstein distance. Because the L^{2}-Wasserstein distance is a geometric measure of optimal transport theory, our result implies a geometric interpretation of the entropy production. Based on this interpretation, we obtain a thermodynamic trade-off relation between transition time and the entropy production. This thermodynamic trade-off relation is regarded as a thermodynamic speed limit which gives a tighter bound of the entropy production. We also discuss stochastic thermodynamics for the subsystem and derive a lower bound on the partial entropy production as a generalization of the second law of information thermodynamics. Our formalism also provides a geometric picture of the optimal protocol to minimize the entropy production. We illustrate these results by the optimal stochastic heat engine and show a geometrical bound of the efficiency.http://doi.org/10.1103/PhysRevResearch.3.043093 |
| spellingShingle | Muka Nakazato Sosuke Ito Geometrical aspects of entropy production in stochastic thermodynamics based on Wasserstein distance Physical Review Research |
| title | Geometrical aspects of entropy production in stochastic thermodynamics based on Wasserstein distance |
| title_full | Geometrical aspects of entropy production in stochastic thermodynamics based on Wasserstein distance |
| title_fullStr | Geometrical aspects of entropy production in stochastic thermodynamics based on Wasserstein distance |
| title_full_unstemmed | Geometrical aspects of entropy production in stochastic thermodynamics based on Wasserstein distance |
| title_short | Geometrical aspects of entropy production in stochastic thermodynamics based on Wasserstein distance |
| title_sort | geometrical aspects of entropy production in stochastic thermodynamics based on wasserstein distance |
| url | http://doi.org/10.1103/PhysRevResearch.3.043093 |
| work_keys_str_mv | AT mukanakazato geometricalaspectsofentropyproductioninstochasticthermodynamicsbasedonwassersteindistance AT sosukeito geometricalaspectsofentropyproductioninstochasticthermodynamicsbasedonwassersteindistance |