ABSTRACT
The threshold networks described in chapter 5 can be generalized in several ways. One way consists of replacing the transition function by the probability of making a transition toward the different possible states. In this case we speak of probabilistic automata, which are mathematical objects whose behavior resembles that of particles in statistical physics. The quick overview that follows, and that constitutes the first part of this chapter, is not an introduction to statistical thermodynamics, but rather a restatement of some useful notions in the framework of the formalism of automata networks. This restatement will enable us to understand the connection between physical systems and automata networks, particularly in terms of numerical simulations. Both domains are enlightened at the conceptual and methodological levels. We will see that the memorization capacities of the Hopfield model can be “exactly” predicted using the statistical physics approach.
