  The circumstances under which a system reaches thermal equilibrium, and how
to derive this from basic dynamical laws, has been a major question from the
very beginning of thermodynamics and statistical mechanics. Despite
considerable progress, it remains an open problem. Motivated by this issue, we
address the more general question of equilibration. We prove, with virtually
full generality, that reaching equilibrium is a universal property of quantum
systems: Almost any subsystem in interaction with a large enough bath will
reach an equilibrium state and remain close to it for almost all times. We also
prove several general results about other aspects of thermalisation besides
equilibration, for example, that the equilibrium state does not depend on the
detailed micro-state of the bath.
