Equilibration of isolated many-body quantum systems with respect to general distinguishability measures

TL;DR

This paper proves that isolated many-body quantum systems tend to behave like steady states over time, with their observable measurement outcomes becoming practically indistinguishable from equilibrium, even when considering generalized measures of distinguishability.

Contribution

It extends previous equilibration results by incorporating generalized distinguishability measures that account for actual measurement outcome probabilities.

Findings

Systems equilibrate with rare deviations over time

Results hold under broad assumptions about initial states and observables

Generalized measures provide a more realistic assessment of equilibration

Abstract

We demonstrate equilibration of isolated many-body systems in the sense that, after initial transients have died out, the system behaves practically indistinguishable from a time-independent steady state, i.e., non-negligible deviations are unimaginably rare in time. Measuring the distinguishability in terms of quantum mechanical expectation values, results of this type have been previously established under increasingly weak assumptions about the initial disequilibrium, the many-body Hamiltonian, and the considered observables. Here, we further extend these results with respect to generalized distinguishability measures which fully take into account the fact that the actually observed, primary data are not expectation values but rather the probabilistic occurrence of different possible measurement outcomes.