### 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.

Original language | English |
---|---|

Article number | 40006 |

Journal | EPL |

Volume | 107 |

Issue number | 4 |

DOIs | |

Publication status | Published - 2014 Aug 1 |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*EPL*,

*107*(4), [40006]. https://doi.org/10.1209/0295-5075/107/40006

**Typical pure nonequilibrium steady states.** / Monnai, Takaaki; Yuasa, Kazuya.

Research output: Contribution to journal › Article

*EPL*, vol. 107, no. 4, 40006. https://doi.org/10.1209/0295-5075/107/40006

}

TY - JOUR

T1 - Typical pure nonequilibrium steady states

AU - Monnai, Takaaki

AU - Yuasa, Kazuya

PY - 2014/8/1

Y1 - 2014/8/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84907324641&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84907324641&partnerID=8YFLogxK

U2 - 10.1209/0295-5075/107/40006

DO - 10.1209/0295-5075/107/40006

M3 - Article

AN - SCOPUS:84907324641

VL - 107

JO - EPL

JF - EPL

SN - 0295-5075

IS - 4

M1 - 40006

ER -