  We propose and discuss two variants of kinetic particle models - cellular
automata in 1+1 dimensions, which have some appeal due to their simplicity and
intriguing properties which could warrant further research and applications.
The first model is a deterministic and reversible automaton describing two
species of quasiparticles: stable massless matter particles moving with
velocity $\pm 1$ and unstable, standing (zero velocity) field particles. We
discuss two distinct continuity equations for three conserved charges of the
model. While the first two charges and the corresponding currents have support
three (3) lattice sites and represent a lattice analogue of conserved
energy-momentum tensor, we find an additional conserved charge and current with
support of nine (9) sites, implying non-ergodic behaviour and potentially
signalling integrability of the model with a highly nested R-matrix structure.
The second model represents a quantum (or stochastic) deformation of a recently
introduced and studied charged hardpoint lattice gas, where particles of
different binary charge ($\pm 1$) and binary velocity ($\pm 1$) can
nontrivially mix upon elastic collisional scattering. We show that while the
unitary evolution rule of this model does not satisfy the full Yang-Baxter
equation, it still satisfies an intriguing related identity which gives birth
to an infinite set of local conserved operators, the-so-called glider
operators.
