Typicality for Generalized Microcanonical Ensembles

TL;DR

This paper demonstrates that for large quantum systems, the expectation values of observables typically align with ensemble averages, even with unknown initial states, extending to nonequilibrium conditions and subsystems coupled to heat baths.

Contribution

It establishes the typicality of ensemble behavior in quantum systems under broad conditions, including nonequilibrium and weakly coupled subsystems, generalizing the microcanonical ensemble framework.

Findings

Observable expectation values rarely deviate from ensemble averages.

Canonical ensemble is valid for subsystems weakly coupled to large heat baths.

Results hold under both equilibrium and nonequilibrium conditions.

Abstract

For a macroscopic, isolated quantum system in an unknown pure state, the expectation value of any given observable is shown to hardly deviate from the ensemble average with extremely high probability under generic equilibrium and nonequilibrium conditions. Special care is devoted to the uncontrollable microscopic details of the system state. For a subsystem weakly coupled to a large heat bath, the canonical ensemble is recovered under much more general and realistic assumptions than those implicit in the usual microcanonical description of the composite system at equilibrium.