Saturation of entropy production in quantum many-body systems*

Thermalization of isolated quantum systems has been of much interest in this decade. In this study, we investigate the second law of thermodynamics for isolated systems in the long time regime, where the initial state of a heat bath can be a pure state. First, we have rigorously proved that the entropy production, which is the sum of the change in the von Neumann entropy of a subsystem and the heat absorbed from a heat bath, saturates in the long-time regime for a broad class of initial states. Second, we have proved the non-negativity of the entropy production at saturation, by assuming the eigenstate thermalization hypothesis (ETH), which states that even a single energy eigenstate is thermal. We also numerically confirmed that the entropy production saturates at a non-negative value even when the initial state of a heat bath is a single energy eigenstate. Our results reveal fundamental properties of the entropy production in isolated quantum systems at late times. Reference: K. Kaneko, E. Iyoda, T. Sagawa, arXiv:1706.10112.