Generalized speed limits for classical stochastic systems and their applications to relaxation, annealing, and pumping processes
We extend the speed limit of a distance between two states evolving by different generators for quantum systems [K. Suzuki and K. Takahashi, Phys. Rev. Res. 2, 032016(R) (2020)2643-156410.1103/PhysRevResearch.2.032016] to the classical stochastic processes described by the master equation. We demons...
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| Format: | Article |
| Language: | English |
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American Physical Society
2023-03-01
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| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/PhysRevResearch.5.013217 |
| _version_ | 1797210518587441152 |
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| author | Kazutaka Takahashi Yasuhiro Utsumi |
| author_facet | Kazutaka Takahashi Yasuhiro Utsumi |
| author_sort | Kazutaka Takahashi |
| collection | DOAJ |
| description | We extend the speed limit of a distance between two states evolving by different generators for quantum systems [K. Suzuki and K. Takahashi, Phys. Rev. Res. 2, 032016(R) (2020)2643-156410.1103/PhysRevResearch.2.032016] to the classical stochastic processes described by the master equation. We demonstrate that the trace distance between arbitrary evolving states is bounded from above by using a geometrical metric. The geometrical bound reduces to the Fisher information metric for the distance between the time-evolved state and the initial state. We compare the bound in relaxation and annealing processes with a different type of bound known for nonequilibrium thermodynamical systems. For dynamical processes such as annealing and pumping processes, the distance between the time-evolved state and the instantaneous stationary state becomes a proper choice and the bound is represented by the Fisher information metric of the stationary state. The metric is related to the counterdiabatic term defined from the time dependence of the stationary state. |
| first_indexed | 2024-04-24T10:11:52Z |
| format | Article |
| id | doaj.art-85248f4c6b7349b2acb9a3a70ca4b321 |
| institution | Directory Open Access Journal |
| issn | 2643-1564 |
| language | English |
| last_indexed | 2024-04-24T10:11:52Z |
| publishDate | 2023-03-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Research |
| spelling | doaj.art-85248f4c6b7349b2acb9a3a70ca4b3212024-04-12T17:29:41ZengAmerican Physical SocietyPhysical Review Research2643-15642023-03-015101321710.1103/PhysRevResearch.5.013217Generalized speed limits for classical stochastic systems and their applications to relaxation, annealing, and pumping processesKazutaka TakahashiYasuhiro UtsumiWe extend the speed limit of a distance between two states evolving by different generators for quantum systems [K. Suzuki and K. Takahashi, Phys. Rev. Res. 2, 032016(R) (2020)2643-156410.1103/PhysRevResearch.2.032016] to the classical stochastic processes described by the master equation. We demonstrate that the trace distance between arbitrary evolving states is bounded from above by using a geometrical metric. The geometrical bound reduces to the Fisher information metric for the distance between the time-evolved state and the initial state. We compare the bound in relaxation and annealing processes with a different type of bound known for nonequilibrium thermodynamical systems. For dynamical processes such as annealing and pumping processes, the distance between the time-evolved state and the instantaneous stationary state becomes a proper choice and the bound is represented by the Fisher information metric of the stationary state. The metric is related to the counterdiabatic term defined from the time dependence of the stationary state.http://doi.org/10.1103/PhysRevResearch.5.013217 |
| spellingShingle | Kazutaka Takahashi Yasuhiro Utsumi Generalized speed limits for classical stochastic systems and their applications to relaxation, annealing, and pumping processes Physical Review Research |
| title | Generalized speed limits for classical stochastic systems and their applications to relaxation, annealing, and pumping processes |
| title_full | Generalized speed limits for classical stochastic systems and their applications to relaxation, annealing, and pumping processes |
| title_fullStr | Generalized speed limits for classical stochastic systems and their applications to relaxation, annealing, and pumping processes |
| title_full_unstemmed | Generalized speed limits for classical stochastic systems and their applications to relaxation, annealing, and pumping processes |
| title_short | Generalized speed limits for classical stochastic systems and their applications to relaxation, annealing, and pumping processes |
| title_sort | generalized speed limits for classical stochastic systems and their applications to relaxation annealing and pumping processes |
| url | http://doi.org/10.1103/PhysRevResearch.5.013217 |
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