# Quantum non-equilibrium and relaxation to equilibrium for a class of de Broglie-Bohm-type theories

## TL;DR

This paper investigates how certain de Broglie-Bohm-type theories relax to quantum equilibrium, finding that some relax faster than standard theory, which could lead to experimentally distinguishable predictions.

## Contribution

It demonstrates that a specific class of trajectory theories can relax to quantum equilibrium more rapidly than de Broglie-Bohm theory, highlighting potential experimental differences.

## Key findings

- Faster relaxation in certain trajectory theories compared to de Broglie-Bohm theory
- Relaxation speed-up may lead to observable deviations from standard quantum predictions
- Different trajectory theories can have distinct non-equilibrium behaviors

## Abstract

The de Broglie-Bohm theory is about non-relativistic point-particles that move deterministically along trajectories. The theory reproduces the predictions of standard quantum theory, given that the distribution of particles over an ensemble of systems, all described by the same wavefunction $\psi$, equals the quantum equilibrium distribution $|\psi|^2$. Numerical simulations by Valentini and Westman have illustrated that non-equilibrium particle distributions may relax to quantum equilibrium after some time. Here we consider non-equilibrium distributions and their relaxation properties for a particular class of trajectory theories, first studied in detail by Deotto and Ghirardi, that are empirically equivalent to the de Broglie-Bohm theory in quantum equilibrium. For the examples of such theories that we consider, we find a speed-up of the relaxation compared to the ordinary de Broglie-Bohm theory. Hence non-equilibrium predictions that depend strongly on relaxation properties, such as those studied recently by Valentini, may vary for different trajectory theories. As such these theories might be experimentally distinguishable.