We consider the thermal relaxation process of a quantum system attached to 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 nonunitary dynamics, and thus reflects the dissipative nature of irreversibility. Intriguingly, the bound can be evaluated solely in terms of the initial and final states and the system Hamiltonian, thereby providing a feasible way to estimate entropy production without prior knowledge of the underlying coupling structure. This finding refines the second law of thermodynamics and reveals a universal feature of thermal relaxation processes.

• Received 16 March 2021
• Accepted 4 October 2021

DOI:https://doi.org/10.1103/PhysRevLett.127.190601