  We demonstrate that the entanglement entropy area law for free fermion ground
states and the corresponding volume law for highly excited states are related
by a position-momentum duality, thus of the same origin. For a typical excited
state in the thermodynamic limit, we further show that the reduced density
matrix of a subsystem approaches thermal density matrix, provided the
subsystem's linear size is small compared to that of the whole system in all
directions, a property we dub eigenstate typicality. This provides an explicit
example of thermalization via entanglement, and reveals how statistical physics
emerges from a single eigenstate by tracing out a large number of degrees of
freedom.
