Dynamical reduction models and the energy conservation principle

A common feature of dynamical reduction models is the violation of energy conservation principle which usually shows up as a constant increase in time of the energy of isolated systems. Anyway for typical values of the parameters of the models, such a violation is usually so weak that cannot be detected with present-day technology. Despite the reduction mechanism itself seems responsible for this behaviour, we show that this is not a intrinsic property of dynamical reduction models: we exhibit a collapse model such that the energy of isolated systems does not diverge for large times but reaches an asymptotic finite value. This result could be interesting in understanding how to work out relativistic extensions of dynamical reduction models.