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  • Letter
  • Open Access

Information geometry of transitions between quantum nonequilibrium steady states

Artur M. Lacerda1,*, Laetitia P. Bettmann1,†, and John Goold1,2,‡

  • 1School of Physics, Trinity College Dublin, College Green, Dublin 2, D02K8N4, Ireland
  • 2Trinity Quantum Alliance, Unit 16, Trinity Technology and Enterprise Centre, Pearse Street, Dublin 2, D02YN67, Ireland

  • *Contact author: machadoa@tcd.ie
  • †Contact author: bettmanl@tcd.ie
  • ‡Contact author: gooldj@tcd.ie
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Phys. Rev. E 112, L022101 – Published 15 August, 2025

DOI: https://doi.org/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.

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Phys. Rev. E 112, L022101– Published 15 August, 2025
  • Received 22 January 2025
  • Accepted 16 July 2025
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