  Understanding under which conditions physical systems thermalize is a
long-standing question in many-body physics. While generic quantum systems
thermalize, there are known instances where thermalization is hindered, for
example in many-body localized (MBL) systems. Here we introduce a class of
stochastic collision models coupling a many-body system out of thermal
equilibrium to an external heat bath. We derive upper and lower bounds on the
size of the bath required to thermalize the system via such models, under
certain assumptions on the Hamiltonian. We use these bounds, expressed in terms
of the max-relative entropy, to characterize the robustness of MBL systems
against externally-induced thermalization. Our bounds are derived within the
framework of resource theories using the convex split lemma, a recent tool
developed in quantum information. We apply our results to the disordered
Heisenberg chain, and numerically study the robustness of its MBL phase in
terms of the required bath size.
