In order to analyse flows of information in the microscopic dynamics of spatially extended systems, we have developed a formalism that under certain circumstances defines a local information or entropy quantity and an associated information flow.
In the present version, the framework applies to discrete one-dimensional dynamical systems with a local update rule, i.e., cellular automata. The dynamics studied possess a certain degree of reversibility, a natural assumption for microscopic dynamics of physical or chemical systems. The cellular automata are assumed to be surjective, i.e., each infinite spatial state has only a finite number of preimages.
For the mathematical details and a formal presentation, we refer to the published paper [Helvik et al, 2007]. The following gives a brief summary of the formalism.