Typical pure nonequilibrium steady states and irreversibility for quantum transports

TL;DR

This paper demonstrates that typical pure states in a large quantum system can represent nonequilibrium steady states (NESS), highlighting the role of irreversibility in the relaxation process to NESS.

Contribution

It extends the concept of typicality from equilibrium to nonequilibrium steady states in quantum systems, showing pure states can represent NESS.

Findings

Typical pure states accurately describe NESS.

Irreversible relaxation is crucial for the typicality of pure NESS.

Large Hilbert space sampling captures NESS properties.

Abstract

It is known that each single typical pure state in an energy shell of a large isolated quantum system well represents a thermal equilibrium state of the system. We show that such typicality holds also for nonequilibrium steady states (NESS's). We consider a small quantum system coupled to multiple infinite 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 to be sampled randomly and show that the typical pure states well describe the NESS. We also point out that the irreversible relaxation to the unique NESS is important to the typicality of the pure NESS's.