Entropy of small subsystems in thermalizing systems

TL;DR

This paper derives an analytical formula for the entropy of small subsystems in thermalizing quantum systems, linking microscopic Hamiltonian parameters to subsystem entropy and explaining recent numerical observations.

Contribution

It provides the first analytical expression for subsystem entropy in thermalizing systems under the eigenstate thermalization hypothesis.

Findings

Derived an explicit formula for subsystem entropy

Connected microscopic parameters to macroscopic entropy behavior

Validated results with recent numerical simulations

Abstract

We study the entropy of small subsystems in thermalizing quantum many-body systems governed by local Hamiltonians. Assuming the eigenstate thermalization hypothesis, we derive an analytical formula for the von Neumann entropy of equilibrated subsystems. This formula reveals how subsystem entropy depends on the microscopic parameters of the Hamiltonian and the macroscopic properties of the initial state. Furthermore, our results provide a theoretical explanation for recent numerical findings by Maceira and L\"auchli, obtained via exact diagonalization.