  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.

Statistical Mechanics;Quantum Physics