Fluctuations of subsystem entropies at late times

TL;DR

This paper investigates the late-time fluctuations of subsystem entropies in quantum many-body systems, revealing significant differences from classical behavior and implications for the rarity of fluctuations and the Boltzmann brain paradox.

Contribution

It provides a combined analytical and numerical analysis of entropy fluctuation statistics in quantum systems, highlighting suppression mechanisms and late-time behavior.

Findings

Entropy fluctuation probability is suppressed by the Hilbert space dimension.

Suppression of fluctuations increases over time, saturating at late times.

Quantum systems reduce the likelihood of rare fluctuations compared to classical systems.

Abstract

We study the fluctuations of subsystem entropies in closed quantum many-body systems after thermalization. Using a combination of analytics and numerics for both random quantum circuits and Hamiltonian dynamics, we find that the statistics of such entropy fluctuations is drastically different than in the classical setting. For instance, shortly after a system thermalizes, the probability of entropy fluctuations for a subregion is suppressed in the dimension of the Hilbert space of the complementary subregion. This suppression becomes increasingly stringent as a function of time, ultimately depending on the exponential of the Hilbert space dimension, until extremely late times when the amount of suppression saturates. We also use our results to estimate the total number of rare fluctuations at large timescales. We find that the "Boltzmann brain" paradox is largely ameliorated in quantum many-body systems, in contrast with the classical setting.