  The non-extensive statistical mechanics has been applied to describe a
variety of complex systems with inherent correlations and feedback loops. Here
we present a dynamical model based on previously proposed static model
exhibiting in the thermodynamic limit the extensivity of the Tsallis entropy
with q<1 as well as a q-Gaussian distribution. The dynamical model consists of
a one-dimensional ring of particles characterized by correlated binary random
variables, which are allowed to flip according to a simple random walk rule.
The proposed dynamical model provides an insight how a mesoscopic dynamics
characterized by the non-extensive statistical mechanics could emerge from a
microscopic description of the system.
