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We propose and discuss two variants of kinetic particle models - cellularautomata in 1+1 dimensions, which have some appeal due to their simplicity andintriguing properties which could warrant further research and applications.The first model is a deterministic and reversible automaton describing twospecies of quasiparticles: stable massless matter particles moving withvelocity $\pm 1$ and unstable, standing (zero velocity) field particles. Wediscuss two distinct continuity equations for three conserved charges of themodel. While the first two charges and the corresponding currents have supportthree (3) lattice sites and represent a lattice analogue of conservedenergy-momentum tensor, we find an additional conserved charge and current withsupport of nine (9) sites, implying non-ergodic behaviour and potentiallysignalling integrability of the model with a highly nested R-matrix structure.The second model represents a quantum (or stochastic) deformation of a recentlyintroduced and studied charged hardpoint lattice gas, where particles ofdifferent binary charge ($\pm 1$) and binary velocity ($\pm 1$) cannontrivially mix upon elastic collisional scattering. We show that while theunitary evolution rule of this model does not satisfy the full Yang-Baxterequation, it still satisfies an intriguing related identity which gives birthto an infinite set of local conserved operators, the-so-called glideroperators.

On two non-ergodic reversible cellular automata, one classical, the other quantum