# Classical Lieb-Robinson Bound for Estimating Equilibration Timescales of Isolated Quantum Systems

## TL;DR

This paper establishes a classical Lieb-Robinson bound for isolated quantum systems, linking locality to equilibration timescales by mapping quantum dynamics onto a classical oscillator network.

## Contribution

It introduces a novel Lieb-Robinson bound that incorporates locality, providing a new method to estimate quantum equilibration times based on the system's Hamiltonian and observables.

## Key findings

- Locality increases equilibration timescales.
- The bound applies to a classical oscillator network representation.
- More local systems equilibrate more slowly.

## Abstract

We study equilibration of an isolated quantum system by mapping it onto a network of classical oscillators in Hilbert space. By choosing a suitable basis for this mapping, the degree of locality of the quantum system reflects in the sparseness of the network. We derive a Lieb-Robinson bound on the speed of propagation across the classical network, which allows us to estimate the timescale at which the quantum system equilibrates. The bound contains a parameter that quantifies the degree of locality of the Hamiltonian and the observable. Locality was disregarded in earlier studies of equilibration times, and is believed to be a key ingredient for making contact with the majority of physically realistic models. The more local the Hamiltonian and observables, the longer the equilibration timescale predicted by the bound.