Title: The local relaxation and correlation production in the quantum Ising model

Abstract: Isolated quantum systems follow the unitary evolution, which guarantees the full many body state always keeps a constant entropy as its initial one. Here we consider the local dynamics of a quantum Ising model with a finite size. It turns out, for both strong and weak coupling situations, the dynamics of local observables exhibits similar relaxation behavior as the macroscopic thermodynamics, which is called the local relaxation; after a certain typical time, the relaxation behavior suddenly changes and appears random, which is referred as a recurrence. Besides, we find that the total correlation entropy of this system approximately exhibit a monotonic increasing envelope in both strong and weak coupling cases, which is quite similar as the irreversible entropy production in the standard macroscopic thermodynamics.