  We consider the reversible exclusion process with reservoirs on arbitrary
networks. We characterize the spectral gap, mixing time, and mixing window of
the process, in terms of certain simple statistics of the underlying network.
Among other consequences, we establish a non-conservative analogue of Aldous's
spectral gap conjecture, and we show that cutoff occurs if and only if the
product condition is satisfied. We illustrate this by providing explicit
cutoffs on discrete lattices of arbitrary dimensions and boundary conditions,
which substantially generalize recent one-dimensional results. We also obtain
cutoff phenomena in relative entropy, Hilbert norm, separation distance and
supremum norm. Our proof exploits negative dependence in a novel, simple way to
reduce the understanding of the whole process to that of single-site marginals.
We believe that this approach will find other applications.
