Asymptotic reversibility of thermal operations for interacting quantum spin systems via generalized quantum Stein’s lemma

For quantum spin systems in any spatial dimension with a local, translation-invariant Hamiltonian, we prove that asymptotic state convertibility from to another one by thermodynamically feasible class of dynamics, called thermal operations, is completely characterized the Kullback-Leibler (KL) divergence rate, if and spatially ergodic. Our proof consists two parts phrased terms branch information theory resource theory. First, states, for which min max R\'enyi divergences collapse approximately single value, can be reversibly converted into operations aid small source coherence. Second, these asymptotically KL rate ergodic state. We show this via generalization Stein's lemma hypothesis testing beyond independent identically distributed (i.i.d.) situations. result implies serves as thermodynamic potential provides complete characterization states many-body limit, including out-of-equilibrium fully