Purity is not eternal in theories with Planck-scale deformed symmetries

Theories with Planck-scale-deformed symmetries exhibit quantum time evolution in which purity of the density matrix is not preserved. In particular we show that the nontrivial structure of momentum space of these models is reflected in a deformed action of translation generators on operators. Such action in the case of time-translation generators leads to a Lindblad-like evolution equation for density matrices when expanded at leading order in the Planckian deformation parameter. This evolution equation is covariant under the deformed realization of Lorentz symmetries characterizing these models. © 2014 American Physical Society.