Information geometry of transitions between quantum nonequilibrium steady states
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908550573326336 |
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| author | Lacerda, Artur M. Bettmann, Laetitia P. Goold, John |
| author_facet | Lacerda, Artur M. Bettmann, Laetitia P. Goold, John |
| contents | In a transition between nonequilibrium steady states, the entropic cost associated with the maintenance of steady-state currents can be distinguished from that arising from the transition itself through the concepts of excess/housekeeping entropy flux and adiabatic/nonadiabatic entropy production. The thermodynamics of this transition is embodied by the Hatano-Sasa relation. In this letter, we show that for a slow transition between quantum nonequilibrium steady states the nonadiabatic entropy production is, to leading order, given by the path action with respect to a Riemannian metric in the parameter space which can be connected to the Kubo-Mori-Bogoliubov quantum Fisher information. We then demonstrate how to obtain minimally dissipative paths by solving the associated geodesic equation and illustrate the procedure with a simple example of a three-level maser. Furthermore, by identifying the quantum Fisher information with respect to time as a metric in state space, we derive an upper bound on the excess entropy flux that holds for arbitrarily fast processes. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2501_08858 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Information geometry of transitions between quantum nonequilibrium steady states Lacerda, Artur M. Bettmann, Laetitia P. Goold, John Quantum Physics Statistical Mechanics In a transition between nonequilibrium steady states, the entropic cost associated with the maintenance of steady-state currents can be distinguished from that arising from the transition itself through the concepts of excess/housekeeping entropy flux and adiabatic/nonadiabatic entropy production. The thermodynamics of this transition is embodied by the Hatano-Sasa relation. In this letter, we show that for a slow transition between quantum nonequilibrium steady states the nonadiabatic entropy production is, to leading order, given by the path action with respect to a Riemannian metric in the parameter space which can be connected to the Kubo-Mori-Bogoliubov quantum Fisher information. We then demonstrate how to obtain minimally dissipative paths by solving the associated geodesic equation and illustrate the procedure with a simple example of a three-level maser. Furthermore, by identifying the quantum Fisher information with respect to time as a metric in state space, we derive an upper bound on the excess entropy flux that holds for arbitrarily fast processes. |
| title | Information geometry of transitions between quantum nonequilibrium steady states |
| topic | Quantum Physics Statistical Mechanics |
| url | https://arxiv.org/abs/2501.08858 |