On thermalization in many-body classical Floquet systems

TL;DR

This paper proves that a broad class of classical many-body Floquet systems inevitably thermalize to infinite temperature, with the only exception being the presence of time-periodic local observables.

Contribution

It introduces an infinite set of classical many-body Floquet systems of algebraic origin for which thermalization can be rigorously proven.

Findings

Gibbs states heat up to infinite temperature over time

Thermalization is obstructed only by local observables that are periodic in time

The results align with physical intuition about thermalization in driven systems

Abstract

It is expected that a generic closed many-body system prepared in a well-behaved initial state and subjected to a periodic drive will eventually thermalize, i.e. approach the state of maximal entropy. This property, while compatible with and even demanded by the physical intuition, is much stronger than ergodicity or mixing and is difficult to justify mathematically. We describe an infinite set of classical many-body Floquet systems of algebraic origin for which thermalization of very general initial states can be proved. For example, we show that a Gibbs state of any sufficiently uniform local differentiable Hamiltonian heats up to infinite temperature at long times. We show that in agreement with the physical intuition, the only obstruction to thermalization is the existence of local observables which are periodic in time.