Characterizing the spontaneous collapse of a wavefunction through entropy production

Objective-collapse models are a unified dynamics approach to solve the so called “measurement problem” of Quantum Mechanics, namely the conflicting nature of the Schrӧdinger equation and the wave function collapse postulate. Two of the most studied of such models, the Continuous Spontaneous Localization (CSL) models and the Diόsi-Penrose (DP) model, share a similar mathematical structure. While in the CSL model the origin of the noise responsible for the collapse is not discussed, in the DP model this is related to gravity. In our work, we study the CSL and DP models from a different perspective, investigating the phenomenology leading to the non-conservation of energy predicted by these theories from the viewpoint of non-equilibrium thermodynamics. 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 a thermodynamic consistent dynamics is possible only if the asymptotic state has infinite temperature. We then repeat the analysis for a dissipative generalization of the models, for which it is possible to characterize the equilibration process in the large temperature limit. In particular, after a preliminary study in the Gaussian limit of the dynamics, we also study the consequences of non-Gaussian effects in the equilibration process.