Stability of Quantum Statistical Ensembles with Respect to Local Measurements

TL;DR

This paper proposes a stability criterion for quantum statistical ensembles, demonstrating that canonical ensembles are nearly stable while broader distributions are not, thus supporting the use of narrow energy distribution ensembles in quantum statistical physics.

Contribution

It introduces a stability criterion for quantum ensembles and applies it to show the near stability of canonical ensembles in quantum systems.

Findings

Canonical ensemble is nearly stable under local measurements

Broader energy distributions are not stable

Supports use of narrow energy distribution ensembles in quantum physics

Abstract

We introduce a stability criterion for quantum statistical ensembles describing macroscopic systems. An ensemble is called "stable" when a small number of local measurements cannot significantly modify the probability distribution of the total energy of the system. We apply this criterion to lattices of spins-1/2, thereby showing that the canonical ensemble is nearly stable, whereas statistical ensembles with much broader energy distributions are not stable. In the context of the foundations of quantum statistical physics, this result justifies the use of statistical ensembles with narrow energy distributions such as canonical or microcanonical ensembles.