Lower Bound on Irreversibility in Thermal Relaxation of Open Quantum Systems

TL;DR

This paper establishes a universal lower bound on the irreversibility of thermal relaxation in open quantum systems, linking entropy production to state differences and enabling estimation without detailed system knowledge.

Contribution

It introduces a state-based lower bound on entropy production during quantum thermal relaxation, refining the second law and providing a practical estimation method.

Findings

The irreversibility is lower-bounded by a relative entropy between evolved and final states.

The bound depends only on initial and final states and the Hamiltonian.

This approach offers a feasible way to estimate entropy production without detailed coupling information.

Abstract

We consider thermal relaxation process of a quantum system attached to a single or multiple reservoirs. Quantifying the degree of irreversibility by entropy production, we prove that the irreversibility of the thermal relaxation is lower-bounded by a relative entropy between the unitarily-evolved state and the final state. The bound characterizes the state discrepancy induced by the non-unitary dynamics, thus reflecting the dissipative nature of irreversibility. Intriguingly, the bound can be evaluated solely in terms of the initial and final states and the system Hamiltonian; hence, providing a feasible way to estimate entropy production without prior knowledge of the underlying coupling structure. Our finding refines the second law of thermodynamics and reveals a universal feature of thermal relaxation processes.