Typical Pure Nonequilibrium Steady States
arXiv:1404.3359 · doi:10.1209/0295-5075/107/40006
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.
6 pages, 1 figure
References in corpus (25)
- Thermalization and its mechanism for generic isolated quantum systems
- Nonequilibrium fluctuations, fluctuation theorems, and counting statistics in quantum systems
- The foundations of statistical mechanics from entanglement: Individual states vs. averages
- Canonical Typicality
- Quantum mechanical evolution towards thermal equilibrium
- Foundation of Statistical Mechanics under experimentally realistic conditions
- Local emergence of thermal correlations in an isolated quantum many-body system
- From Quantum Dynamics to the Canonical Distribution: General Picture and a Rigorous Example
- Typicality for Generalized Microcanonical Ensembles
- Quantum equilibration in finite time
- Canonical Thermal Pure Quantum State
- Thermal Pure Quantum States at Finite Temperature
- Fluctuation theorem for currents in open quantum systems
- Fluctuation theorem in quantum heat conduction
- On the Approach to Thermal Equilibrium of Macroscopic Quantum Systems
- Observation of grand-canonical number statistics in a photon Bose-Einstein condensate
- Equilibration of isolated macroscopic quantum systems
- On the time scales in the approach to equilibrium of macroscopic quantum systems
- Condensate Fluctuations in Trapped Bose Gases: Canonical vs. Microcanonical Ensemble
- Distribution of local entropy in the Hilbert space of bi-partite quantum systems: Origin of Jaynes' principle
- Nonequilibrium Steady State in a Quantum System: One-dimensional Transverse Ising Model with Energy Current
- On the speed of fluctuations around thermodynamic equilibrium
- Fluctuation Theorem and Microreversibility in a Quantum Coherent Conductor
- Nonequilibrium Steady States and MacLennan-Zubarev Ensembles in a Quantum Junction System
- General relaxation time of the fidelity for isolated quantum thermodynamic systems