back to the initial configuration after a time $T$, which could be exponentially long and it displays a complex behavior (not chaotic stricto-sensu, see for instance [@grassberger]). More important the probability that an initial condition possesses such a complex behavior is finite [@hans2]. Moreover, Q2R manifests “sensitivity to initial conditions”, that is, if one starts with two distinct, but close, initial conditions, then, they evolve into very different cycles as time evolves [@goles]. In some sense, an initial state explores vastly the phase space justifying the grounds of statistical physics.

In conclusion, the overall picture is : although for a finite size system the deterministic automata Q2R possesses a periodic dynamics so it is not ergodic, there is a huge number of initial conditions that explore vastly the configurational space (this is particularly remarkably for initial conditions of random structure). Therefore, one expects that a master equation approach my be successful.

\(a) ![ \[CycleDraft\] (a) Scheme of a sub-space of constant energy composed by a number of cycles and fixed points. (b) Cartoon of a cycle of period $T$, for which the cycle is composed of $T$ states. ](CartoonCycle.eps "fig:"){width="7cm"}

\(b) ![ \[CycleDraft\] (a) Scheme of a sub-space of constant 