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.