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It is known that each single typical pure state in an energy shell of a largeisolated quantum system well represents a thermal equilibrium state of thesystem. We show that such typicality holds also for nonequilibrium steadystates (NESS's). We consider a small quantum system coupled to multipleinfinite reservoirs. In the long run, the total system reaches a unique NESS.We identify a large Hilbert space from which pure states of the system are tobe sampled randomly and show that the typical pure states well describe theNESS. We also point out that the irreversible relaxation to the unique NESS isimportant to the typicality of the pure NESS's.

Typical pure nonequilibrium steady states and irreversibility for quantum transports