Equilibrium and nonequilibrium in the three-dimensional Q2R cellular automata

Abstract

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.

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.