Observable Statistical Mechanics

TL;DR

This paper introduces a simple, general method based on maximum entropy principles to predict stationary distributions of observables in isolated quantum systems, bypassing detailed energy information.

Contribution

It proposes a novel, computationally efficient approach to determine observable distributions using coarse measurements and maximum entropy, applicable to various quantum models.

Findings

Accurately predicts stationary distributions without detailed energy data.

Works effectively across integrable and chaotic quantum systems.

Validated through extensive numerical experiments on multiple Hamiltonians.

Abstract

Predicting the stationary behavior of observables in isolated many-body quantum systems is a central challenge in quantum statistical mechanics. While one can often use the Gibbs ensemble, which is simple to compute, there are many scenarios where this is not possible and one must instead use another ensemble, such as the diagonal, microcanonical or generalized Gibbs ensembles. However, these all require detailed information about the energy or other conserved quantities to be constructed. Here we propose a general and computationally easy approach to determine the stationary probability distribution of observables with few outcomes. Interpreting coarse measurements at equilibrium as noisy communication channels, we provide general analytical arguments in favor of the applicability of a maximum entropy principle for this class of observables. We show that the resulting theory accurately predicts stationary probability distributions without detailed microscopic information like the energy eigenstates. Extensive numerical experiments on 7 non-weakly interacting spin-1/2 Hamiltonians demonstrate the broad applicability and robustness of this framework in both quantum integrable and chaotic models.