Numerical recipes in C (2nd ed.): the art of scientific computing
Numerical recipes in C (2nd ed.): the art of scientific computing
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We found out the entropy function of the cellular automata traffic models in a single-lane whose particle interaction rules satisfy an exclusion principle, conserve the number of particles, and prevent collisions and overtaking. With it we studied the velocity distributions of the maximum entropy states of these models. As a result, although the velocity updating rules of the Nagel-Schreckenberg traffic model drive it to states far from equilibrium, we found that the velocity distributions and fundamental diagrams of the maximum-entropy states resemble strongly the steady-states of this model at low energies. We found also that entropy as a function of particle density evidences the existence of several flow regimes in these models, with a sharp transition between the free and jammed flows in the high-energy limit. Finally, on the base of the existence of entropy for these models, we conjectured an interpretation like thermodynamics of traffic flow phenomena, and the behaviors of some thermodynamic properties, such as specific heat, isothermal compressibility, and others, are presented.