On the evolution of quantum non-equilibrium in expanding systems

TL;DR

This paper investigates how quantum non-equilibrium states evolve over time in an expanding 2D box within the pilot-wave framework, showing that such states can diverge from equilibrium even if initially close.

Contribution

It demonstrates that quantum non-equilibrium can naturally develop from near-equilibrium states in an expanding system, challenging the assumption of initial equilibrium.

Findings

Quantum ensembles can diverge from equilibrium over time.

Expansion can induce non-equilibrium behavior.

Initial near-equilibrium states may evolve into non-equilibrium.

Abstract

We consider a particle confined in a uniformly expanding two-dimensional square box from the point of the view of the de Broglie-Bohm pilot-wave theory. In particular we study quantum ensembles in which the Born Law is initially violated (quantum non-equilibrium). We show examples of such ensembles that start close to quantum equilibrium, as measured by the standard coarse-grained H-function, but diverge from it with time. We give an explanation of this result and discuss the possibilities that it opens.