Purity is not eternal at the Planck scale

Understand

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.