  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 non-trivial 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.
