Equilibrium and nonequilibrium in the three-dimensional Q2R cellular automata

I study the equilibrium and nonequilibrium dynamics of a conservative and reversible Q2R cellular automata. This system exhibits a configuration space with 2^{2N} states, which grows with the size of the system. In this context, for small size, the phase space has fixed points and cycles. Through numerical studies and using a statistical approach, I can observe stable and unstable behaviors as well as a phase transition around a critical energy E_{c}. I introduce a coupling constant as a perturbation to the classic Q2R model and show through the phase diagram how this modified model exhibits three different phases.