Macroscopic Thermodynamic Reversibility in Quantum Many-Body Systems

The resource theory of thermal operations, an established model for small-scale thermodynamics, provides an extension of equilibrium thermodynamics to nonequilibrium situations. On a translation-invariant lattice with local interactions, we show that ergodic states (i.e. states that have sharp statistics for any translation-invariant observable) can be reversibly converted to and from the thermal state with thermal operations and a small amount of coherence. This proves the emergence of an operationally well-justified thermodynamic potential for this class of states, which includes states that are not in equilibrium. As an intermediate result of independent interest, we show that the gap between the min- and max-relative entropies controls the amount of coherence that is present in the state and that if this gap is small, the state can be approximately reversibly converted to and from the thermal state with a small reference frame. Our results provide a strong link between the abstract resource theory of thermodynamics and more realistic physical systems that go beyond the i.i.d. setting.