  The Eigenstate Thermalization Hypothesis (ETH) has played a major role in
understanding thermodynamic phenomena in closed quantum systems. However, its
connection to the timescale of thermalization for open system dynamics has
remained elusive. This paper establishes a rigorous link between ETH and fast
thermalization to the global Gibbs state. Specifically, we demonstrate fast
thermalization for a system coupled weakly to a bath of quasi-free Fermions
that we refresh periodically. To describe the joint evolution, we derive a
finite-time version of Davies' generator with explicit error bounds and
resource estimates. Our approach exploits a critical feature of ETH: operators
in the energy basis can be modeled by independent random matrices in a
near-diagonal band. This gives quantum expanders at nearby eigenstates of the
Hamiltonian and reduces the problem to a one-dimensional classical random walk
on the energy eigenstates. Our results explain finite-time thermalization in
chaotic open quantum systems.
