Information geometry of transitions between quantum nonequilibrium steady states
arXiv:2501.08858 · doi:10.1103/9f6l-d766
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.
11 pages, 2 figures. Final author version
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