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The Eigenstate Thermalization Hypothesis (ETH) has played a major role inunderstanding thermodynamic phenomena in closed quantum systems. However, itsconnection to the timescale of thermalization for open system dynamics hasremained elusive. This paper establishes a rigorous link between ETH and fastthermalization to the global Gibbs state. Specifically, we demonstrate fastthermalization for a system coupled weakly to a bath of quasi-free Fermionsthat we refresh periodically. To describe the joint evolution, we derive afinite-time version of Davies' generator with explicit error bounds andresource estimates. Our approach exploits a critical feature of ETH: operatorsin the energy basis can be modeled by independent random matrices in anear-diagonal band. This gives quantum expanders at nearby eigenstates of theHamiltonian and reduces the problem to a one-dimensional classical random walkon the energy eigenstates. Our results explain finite-time thermalization inchaotic open quantum systems.

Fast Thermalization from the Eigenstate Thermalization Hypothesis