Non-equilibrium thermodynamics of gravitational objective-collapse models

TL;DR

This paper analyzes entropy production in gravity-related collapse models, revealing unbounded heating in the original model and thermalization in its dissipative extension, with implications for non-equilibrium thermodynamics.

Contribution

It provides a detailed thermodynamic analysis of the Di"osi-Penrose collapse model and introduces a dissipative extension that achieves consistent thermalization.

Findings

Original DP model causes unbounded heating.

Dissipative extension enables thermalization at low dissipation.

Non-Gaussian features are explicitly included in the dynamics.

Abstract

We investigate the entropy production in the Di\'osi-Penrose (DP) model, one of the most extensively studied gravity-related collapse mechanisms, and one of its dissipative extensions. To this end, we analyze the behavior of a single harmonic oscillator, subjected to such collapse mechanisms, focusing on its phase-space dynamics and the time evolution of the entropy production rate, a central quantity in non-equilibrium thermodynamics. Our findings reveal that the original DP model induces unbounded heating, producing dynamics consistent with the Second Law of thermodynamics only under the assumption of an infinite-temperature noise field. In contrast, its dissipative extension achieves physically consistent thermalization in the regime of low dissipation strength. We further our study to address the complete dynamics of the dissipative extension, thus including explicitly non-Gaussian features in the state of the system that lack from the low-dissipation regime, using a short-time approach.