  The emergence of quantum statistical mechanics from individual pure states of
closed many-body systems is currently under intensive investigations. While
most efforts have been put on the impacts of the direct interaction (i.e., the
usual mutual interaction) between particles, here we study systematically and
analytically the impacts of the exchange interaction, that arises from the
particle indistinguishability. We show that this interaction leads an
overwhelming number of Fock states to exhibit a structure, that can be resolved
only by observables adjusted according to system's dynamical properties and
from which thermal distributions emerge. This hidden thermal structure in Fock
space is found to be related to the so-called limit shape of random geometric
objects in mathematics. The structure enables us to uncover, for both ideal and
nonideal Fermi gases, new mechanisms for the emergence of quantum statistical
mechanics from individual eigenstates.
