  We show that typicality holds for a class of nonequilibrium systems, i.e.,
nonequilibrium steady states (NESSs): almost all the pure states properly
sampled from a certain Hilbert space well represent a NESS and characterize its
intrinsic thermal nature. We clarify the relevant Hilbert space from which the
pure states are to be sampled, and construct practically all the typical pure
NESSs. The scattering approach leads us to the natural extension of the
typicality for equilibrium systems. Each pure NESS correctly yields the
expectation values of observables given by the standard ensemble approach. It
means that we can calculate the expectation values in a NESS with only a single
pure NESS. We provide an explicit construction of the typical pure NESS for a
model with two reservoirs, and see that it correctly reproduces the
Landauer-type formula for the current flowing steadily between the reservoirs.
