  We study the nature of and approach to thermal equilibrium in isolated
quantum systems. An individual isolated macroscopic quantum system in a pure or
mixed state is regarded as being in thermal equilibrium if all macroscopic
observables assume rather sharply the values obtained from thermodynamics. Of
such a system (or state) we say that it is in macroscopic thermal equilibrium
(MATE). A stronger requirement than MATE is that even microscopic observables
(i.e., ones referring to a small subsystem) have a probability distribution in
agreement with that obtained from the micro-canonical, or equivalently the
canonical, ensemble for the whole system. Of such a system we say that it is in
microscopic thermal equilibrium (MITE). The distinction between MITE and MATE
is particularly relevant for systems with many-body localization (MBL) for
which the energy eigenfuctions fail to be in MITE while necessarily most of
them, but not all, are in MATE. However, if we consider superpositions of
energy eigenfunctions (i.e., typical wave functions $\psi$) in an energy shell,
then for generic macroscopic systems, including those with MBL, most $\psi$ are
in both MATE and MITE. We explore here the properties of MATE and MITE and
compare the two notions, thereby elaborating on ideas introduced in [Goldstein
et al., Phys.Rev.Lett. 115: 100402 (2015)].
