Typical pure nonequilibrium steady states

¹ Waseda Institute for Advanced Study, Waseda University - Tokyo 169-8050, Japan
² Department of Physics, Waseda University - Tokyo 169-8555, Japan

^(a) monnai@suou.waseda.jp
^(b) yuasa@waseda.jp

Received: 14 April 2014
Accepted: 26 July 2014

Abstract

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.