Characterizing the spontaneous collapse of a wavefunction through entropy production

We investigate the phenomenology leading to the non-conservation of energy of the continuous spontaneous localization (CSL) model from the viewpoint of non-equilibrium thermodynamics, and use such framework to assess the equilibration process entailed by the dissipative formulation of the model (dCSL). As a paradigmatic situation currently addressed in frontier experiments aimed at investigating possible collapse theories, we consider a one-dimensional mechanical oscillator in a thermal state. We perform our analysis in the phase space of the oscillator, where the entropy production rate, a non-equilibrium quantity used to characterize irreversibility, can be conveniently analyzed. We show that the CSL model violates Clausius law, as it exhibits a negative entropy production rate, while the dCSL model reaches equilibrium consistently only under certain dynamical conditions, thus allowing us to identify the values -- in the parameter space -- where the latter mechanism can be faithfully used to describe a thermodynamically consistent phenomenon.