Information geometry approach to quantum stochastic thermodynamics

Area of Science:

• Quantum Information Theory
• Statistical Mechanics
• Information Geometry

Background:

• Recent studies highlight connections between information geometry and stochastic thermodynamics.
• Fisher Information (FI) with respect to time is a key concept linking these fields.
• The quantum Fisher metric in Hilbert space is nonunique, necessitating decomposition methods.

Purpose of the Study:

• To decompose quantum Fisher information (QFI) into metric-independent and metric-dependent parts.
• To establish links between the incoherent component of QFI, entropic acceleration, and thermodynamic quantities.
• To generalize classical uncertainty relations and entropy rate bounds to quantum systems and analyze quantum thermodynamic phenomena.

Main Methods:

• Decomposition of QFI into incoherent and coherent contributions.
• Analysis of generalized GKS-L (Gorini-Kossakowski-Sudarshan-Lindblad) dynamics.
• Application of information-geometric analysis to quantum systems and the Mpemba effect.

Main Results:

• The incoherent component of QFI is directly linked to entropic acceleration and thermodynamic forces in GKSL dynamics.
• A classical uncertainty relation is tightened and shown to hold for quantum systems.
• A generalized geometric bound on entropy rate for far-from-equilibrium processes is derived, including a quantum contribution.

Conclusions:

• The framework successfully captures thermodynamic phenomena, exemplified by its application to the quantum-thermodynamic Mpemba effect.
• The study provides a unified information-geometric approach to quantum thermodynamics.
• Established parallels between classical and quantum stochastic thermodynamics are reinforced.