  Based on the view that thermal equilibrium should be characterized through
macroscopic observations, we develop a general theory about typicality of
thermal equilibrium and the approach to thermal equilibrium in macroscopic
quantum systems. We first formulate the notion that a pure state in an isolated
quantum system represents thermal equilibrium. Then by assuming, or proving in
certain classes of nontrivial models (including that of two bodies in thermal
contact), large-deviation type bounds (which we call thermodynamic bounds) for
the microcanonical ensemble, we prove that to represent thermal equilibrium is
a typical property for pure states in the microcanonical energy shell. We
believe that the typicality, along with the empirical success of statistical
mechanics, provides a sound justification of equilibrium statistical mechanics.
We also establish the approach to thermal equilibrium under two different
assumptions; one is that the initial state has a moderate energy distribution,
and the other is the energy eigenstate thermalization hypothesis.
