  Inside a closed many-body system undergoing the unitary evolution, a small
partition of the whole system exhibits a local relaxation. If the total degrees
of freedom of the whole system is a large but finite number, such a local
relaxation would come across a recurrence after a certain time, namely, the
dynamics of the local system suddenly appear random after a well-ordered
oscillatory decay process. It is found in this paper, for a collection of $N$
two-level systems (TLSs), the local relaxation of one TLS within has a
hierarchy structure hiding in the randomness after such a recurrence: similar
recurrences appear in a periodical way, and the later recurrence brings in
stronger randomness than the previous one. Both analytical and numerical
results that we obtained well explains such hierarchy recurrences: the
population of the local TLS (as an open system) diffuses out and regathers back
periodically due the finite-size effect of the bath [the remaining $(N-1)$
TLSs]. We also find that the total correlation entropy, which sums up the
entropy of all the $N$ TLSs, approximately exhibit a monotonic increase; in
contrast, the entropy of each single TLS increases and decreases from time to
time, and the entropy of the whole $N$-body system keeps constant during the
unitary evolution.

Quantum Physics;Statistical Mechanics