  Introduced by Lu and Yau (CMP, 1993), the martingale decomposition method is
a powerful recursive strategy that has produced sharp log-Sobolev inequalities
for homogeneous particle systems. However, the intractability of certain
covariance terms has so far precluded applications to heterogeneous models.
Here we demonstrate that the existence of an appropriate coupling can be
exploited to bypass this limitation effortlessly. Our main result is a
dimension-free modified log-Sobolev inequality for zero-range processes on the
complete graph, under the only requirement that all rate increments lie in a
compact subset of $(0,\infty)$. This settles an open problem raised by Caputo
and Posta (PTRF, 2007) and reiterated by Caputo, Dai Pra and Posta (AIHP,
2009). We believe that our approach is simple enough to be applicable to many
systems.
