Abstract
We consider brain activity from an information theoretic perspective. We analyze the information processing in the brain, considering the optimality of Shannon entropy transport using the Monge-Kantorovich framework. It is proposed that some of these processes satisfy an optimal transport of informational entropy condition. This optimality condition allows us to derive an equation of the Monge-Ampère type for the information flow that accounts for the branching structure of neurons via the linearization of this equation. Based on this fact, we discuss a version of Murray's law in this context.