# Measurement-Induced Dynamical Quantum Thermalization

## TL;DR

This paper explores how quantum systems reach thermal equilibrium through measurements, showing that entanglement with an effective bath leads to thermal behavior over time.

## Contribution

The study introduces a new mechanism for quantum thermalization via measurement-induced entanglement with an effective bath.

## Key findings

- Measurement-induced entanglement leads to a bi-exponential approach to thermal equilibrium.
- Thermalization occurs for both local and non-local observables.
- The process is independent of the initial quantum state.

## Abstract

One of the fundamental problems of quantum statistical physics is how an ideally isolated quantum system can ever reach thermal equilibrium behavior despite the unitary time evolution of quantum-mechanical systems. Here, we study, via explicit time evolution for the generic model system of an interacting, trapped Bose gas with discrete single-particle levels, how the measurement of one or more observables subdivides the system into observed and non-observed Hilbert subspaces and the tracing over the non-measured quantum numbers defines an effective, thermodynamic bath, induces the entanglement of the observed Hilbert subspace with the bath, and leads to a bi-exponential approach of the entanglement entropy and of the measured observables to thermal equilibrium behavior as a function of time. We find this to be more generally fulfilled than in the scenario of the eigenstate thermalization hypothesis (ETH), namely for both local particle occupation numbers and non-local density correlation functions, and independent of the specific initial quantum state of the time evolution.