if ubiquitous” behavior, upon changing the connectivity [@Dodds; @Harris].

The main goal of the present study is that of reformulating the opinion formation models mentioned above [@bagnoli2013; @bagnoli2015], in terms of a parallel, nonlinear Ising model both on a regular lattice, where the spin at any site is influenced by its nearest neighbors, and on small-world networks.

In the first case the mean-field behavior of the magnetization is described by a nonlinear equation for which chaos can be evaluated by the Lyapunov exponent [@ott02], which is a measure of the stability of trajectories.

The Lyapunov exponent is the time average of the growth rate of an initial infinitesimal perturbation of a trajectory. Clearly, this quantity cannot be simply defined for stochastic systems, since in this case one would essentially measure the effects of the noise. However, in many cases and in particular the present one, we would like to compare the dynamical properties of a stochastic microscopic model and its mean-field approximation. We show here that the Boltzmann’s entropy of an aggregate variable like the magnetization is a quantity that can be defined for both deterministic and stochastic systems. In the first case, Boltzmann’s entropy can be used as a 