Information geometry of transitions between quantum nonequilibrium steady states

TL;DR

This paper explores the geometric structure of quantum nonequilibrium steady state transitions, linking entropy production to quantum Fisher information and providing methods to find minimally dissipative paths.

Contribution

It introduces a quantum geometric framework connecting entropy production to the quantum Fisher information, enabling optimization of transition paths.

Findings

Nonadiabatic entropy production relates to a Riemannian metric derived from quantum Fisher information.

Minimally dissipative transition paths can be obtained by solving geodesic equations.

An upper bound on excess entropy flux is derived for fast quantum processes.

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.