Information geometry approach to quantum stochastic thermodynamics

TL;DR

This paper explores the connection between information geometry and quantum stochastic thermodynamics, decomposing quantum Fisher information into incoherent and coherent parts, and applying this to analyze thermodynamic phenomena like the quantum Mpemba effect.

Contribution

It introduces a novel decomposition of quantum Fisher information, linking it to thermodynamic quantities and extending classical geometric bounds to quantum systems.

Findings

Incoherent QFI relates to entropic acceleration.

Classical uncertainty relations hold for quantum systems.

Quantum geometric bounds help analyze the Mpemba effect.

Abstract

Recent advancements have revealed new links between information geometry and classical stochastic thermodynamics, particularly through the Fisher information (FI) with respect to time. Recognizing the non-uniqueness of the quantum Fisher metric in Hilbert space, we exploit the fact that any quantum Fisher information (QFI) can be decomposed into a metric-independent incoherent part and a metric-dependent coherent contribution. We demonstrate that the incoherent component of any QFI can be directly linked to entropic acceleration, and for GKSL dynamics with local detailed balance, to the rate of change of generalised thermodynamic forces and entropic flow, paralleling the classical results. Furthermore, we tighten a classical uncertainty relation between the geometric uncertainty of a path in state space and the time-averaged rate of information change and demonstrate that it also holds for quantum systems. We generalise a classical geometric bound on the entropy rate for far-from-equilibrium processes by incorporating a non-negative quantum contribution that arises from the geometric action due to coherent dynamics. Finally, we apply an information-geometric analysis to the recently proposed quantum-thermodynamic Mpemba effect, demonstrating this framework's ability to capture thermodynamic phenomena.