Non-equilibrium thermodynamics of gravitational objective-collapse models

We investigate the entropy production in the Diósi-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 nonequilibrium 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. Using a short-time approach, 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.