Force-current structure in Markovian open quantum systems and its applications: geometric housekeeping-excess decomposition and thermodynamic trade-off relations

TL;DR

This paper develops a quantum thermodynamic framework using anti-Hermitian operators to represent forces and currents, extending classical concepts to quantum systems and deriving new relations like the quantum housekeeping-excess decomposition.

Contribution

It introduces a novel operator-based structure for quantum thermodynamics that generalizes classical entropy production and extends stochastic thermodynamics results.

Findings

Entropy production rate expressed as force-current product in quantum systems

Extension of classical thermodynamic decompositions to quantum regimes

Derivation of quantum trade-off relations including the quantum uncertainty bounds

Abstract

Thermodynamic force and irreversible current are the foundational concepts of classical nonequilibrium thermodynamics. Entropy production rate is provided by their product in classical systems, ranging from mesoscopic to macroscopic systems. However, there is no complete quantum extension of such a structure that respects quantum mechanics. In this paper, we propose anti-Hermitian operators that represent currents and forces accompanied by a gradient structure in open quantum systems described by the quantum master equation. We prove that the entropy production rate is given by the product of the force and current operators, which extends the canonical expression of the entropy production rate in the classical systems. The framework constitutes a comprehensive analogy with the nonequilibrium thermodynamics of discrete classical systems. We also show that the structure leads to the extensions of some results in stochastic thermodynamics: the geometric housekeeping-excess decomposition of entropy production and thermodynamic trade-off relations such as the thermodynamic uncertainty relation and the dissipation-time uncertainty relation. In discussing the trade-off relations, we will introduce a measure of fluctuation, which we term the quantum diffusivity.