Information geometry of transitions between quantum nonequilibrium steady states

• URL: http://arxiv.org/abs/2501.08858v1
• Date: Wed, 15 Jan 2025 15:13:09 GMT
• Title: Information geometry of transitions between quantum nonequilibrium steady states
• Authors: Artur M. Lacerda, Laetitia P. Bettmann, John Goold,
• Abstract summary: We show that for a slow transition between quantum nonequilibrium steady states the nonadiabatic entropy production is to leading order. We derive an upper bound on the excess entropy flux that holds for arbitrarily fast processes.
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• Abstract: 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.

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