Boundary-induced classical Generalized Gibbs Ensemble with angular momentum

TL;DR

This paper explores how boundary shape influences thermalization in a classical hard disk system, revealing that circular boundaries lead to a Generalized Gibbs Ensemble with angular momentum, violating ergodicity and time-reversal symmetry.

Contribution

It demonstrates that boundary geometry determines the emergent statistical ensemble, showing circular boundaries induce a GGE with angular momentum, unlike square boundaries which lead to Gibbs ensemble.

Findings

Circular boundaries lead to GGE with angular momentum.

Boundary shape affects ergodicity and time-reversal invariance.

Near-boundary condensation occurs in the GGE regime.

Abstract

We investigate the impact of the boundary shape on the thermalization behavior of a confined system of classical hard disks at low packing fraction and thus in the gas regime. We use both analytical calculations and numerical simulations, and leveraging on the insights from the maximum entropy principle, we explore how the geometry of the boundary influences the thermal equilibration process in such systems. Our simulations involve hard disks confined within varying boundary shapes, using both event-driven and time-driven simulations, ranging from conventional square boundaries to circular boundaries, showing that the two converge to different ensembles. The former converges to the Gibbs Ensemble, while the latter converges to the Generalized Gibbs Ensemble (GGE), with angular momentum as the extra conserved quantity. We introduce an order parameter to characterize the deviations from the Gibbs ensemble, and show that the GGE is not time-reversal invariant, it violates ergodicity and leads to a near-boundary condensation phenomenon. Because of this, we argue that Monte Carlo methods should include angular momentum in this situation. We conclude by discussing how these results lead to peculiar violations of the Bohr-van Leeuwen theorem.