  We investigate the relaxation dynamics of an interacting Stark-localized
system coupled to a dephasing bath, and compare its behavior to the
conventional disorder-induced many body localized system. Specifically, we
study the dynamics of population imbalance between even and odd sites, and the
growth of the von Neumann entropy. For a large potential gradient, the
imbalance is found to decay on a time scale that grows quadratically with the
Wannier-Stark tilt. For the non-interacting system, it shows an exponential
decay, which becomes a stretched exponential decay in the presence of finite
interactions. This is different from a system with disorder-induced
localization, where the imbalance exhibits a stretched exponential decay also
for vanishing interactions. As another clear qualitative difference, we do not
find a logarithmically slow growth of the von-Neumann entropy as it is found
for the disordered system. Our findings can immediately be tested
experimentally with ultracold atoms in optical lattices.
