Information Processing in the Brain as Optimal Entropy Transport: A Theoretical Approach

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.

Keywords

• informational entropy
• neuroscience
• Monge–Ampère equation
• optimal transport
• variational calculus
• Murray’s law