Probabilistic model of N correlated binary random variables and non-extensive statistical mechanics

•We consider a simple model consisting of a one-dimensional spin chain.•The model exhibits the extensivity of the Tsallis generalized entropy.•The model yields q-Gaussian distribution in the limit of large number of particles.•The values of q, obtained from the entropy and from the distribution are different.

The framework of non-extensive statistical mechanics, proposed by Tsallis, has been used to describe a variety of systems. The non-extensive statistical mechanics is usually introduced in a formal way, thus simple models exhibiting some important properties described by the non-extensive statistical mechanics are useful to provide deeper physical insights. In this article we present a simple model, consisting of a one-dimensional chain of particles characterized by binary random variables, that exhibits both the extensivity of the generalized entropy with q<1q<1 and a q-Gaussian distribution in the limit of the large number of particles.