States of open quantum systems usually decay continuously under environmental
interactions. Quantum Markov semigroups model such processes in dissipative
environments. It is known that a finite-dimensional quantum Markov semigroup
with detailed balance induces exponential decay toward a subspace of invariant
or fully decayed states, under what are called modified logarithmic Sobolev
inequalities. We analyze continuous processes that combine coherent and
stochastic processes, breaking detailed balance. We find counterexamples to
analogous decay bounds for these processes. Through analogs of the quantum Zeno
effect, noise can suppress interactions that would spread it. Faster decay of a
subsystem may thereby slow overall decay. Hence the relationship between the
strength of noise on a part and induced decay on the whole system is often
non-monotonic. We observe this interplay numerically and its discrete analog
experimentally on IBM Q systems. Our main results then explain and generalize
the phenomenon theoretically. In contrast, we also lower bound decay rates
above any given timescale by combining estimates for simpler, effective
processes across times.Comment: 40 pages, 7 figures. Update removes some content on discrete
compositions of channels, revises and corrects some mathematical content, and
generalizes some main theorem