  We consider departures from hamiltonian dynamics in the evolution of neutral
kaons due to their interactions with environment that generate entanglement
among them. We propose a phenomenological model of stochastic re-scattering and
estimate the coefficients of the effective hamiltonian and decoherence terms.
Finally we analyze the interplay between the weak interaction and matter
effects and propose the observables suitable to measure the matter
characteristics of CPT violation and decoherence.
