We consider the notion of thermal equilibrium for an individual closed
macroscopic quantum system in a pure state, i.e., described by a wave function.
The macroscopic properties in thermal equilibrium of such a system, determined
by its wave function, must be the same as those obtained from thermodynamics,
e.g., spatial uniformity of temperature and chemical potential. When this is
true we say that the system is in macroscopic thermal equilibrium (MATE). Such
a system may however not be in microscopic thermal equilibrium (MITE). The
latter requires that the reduced density matrices of small subsystems be close
to those obtained from the microcanonical, equivalently the canonical, ensemble
for the whole system. The distinction between MITE and MATE is particularly
relevant for systems with many-body localization (MBL) for which the energy
eigenfunctions fail to be in MITE while necessarily most of them, but not all,
are in MATE. We note however that for generic macroscopic systems, including
those with MBL, most wave functions in an energy shell are in both MATE and
MITE. For a classical macroscopic system, MATE holds for most phase points on
the energy surface, but MITE fails to hold for any phase point
