  In this work, we show how Gibbs or thermal states appear dynamically in
closed quantum many-body systems, building on the program of dynamical
typicality. We introduce a novel perturbation theorem for physically relevant
weak system-bath couplings that is applicable even in the thermodynamic limit.
We identify conditions under which thermalization happens and discuss the
underlying physics. Based on these results, we also present a fully general
quantum algorithm for preparing Gibbs states on a quantum computer with a
certified runtime and error bound. This complements quantum Metropolis
algorithms, which are expected to be efficient but have no known runtime
estimates and only work for local Hamiltonians.
