Information geometry approach to quantum stochastic thermodynamics

• URL: http://arxiv.org/abs/2409.06083v1
• Date: Mon, 9 Sep 2024 21:34:54 GMT
• Title: Information geometry approach to quantum stochastic thermodynamics
• Authors: Laetitia P. Bettmann, John Goold,
• Abstract summary: 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 show that the classical uncertainty relation between the geometric uncertainty of a path in state space and the time-integrated rate of information change also holds for quantum systems.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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 generalized thermodynamic forces and entropic flow, paralleling the classical results. Furthermore, we show that the classical uncertainty relation between the geometric uncertainty of a path in state space and the time-integrated rate of information change 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.

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