Fate of Duplicated Neural Structures

Statistical mechanics determines the abundance of different arrangements of matter depending on cost-benefit balances. Its formalism and phenomenology percolate throughout biological processes and set limits to effective computation. Under specific conditions, self-replicating and computationally complex patterns become favored, yielding life, cognition, and Darwinian evolution. Neurons and neural circuits sit at a crossroads between statistical mechanics, computation, and (through their role in cognition) natural selection. Can we establish a {\em statistical physics} of neural circuits? Such theory would tell what kinds of brains to expect under set energetic, evolutionary, and computational conditions. With this big picture in mind, we focus on the fate of duplicated neural circuits. We look at examples from central nervous systems, with a stress on computational thresholds that might prompt this redundancy. We also study a naive cost-benefit balance for duplicated circuits implementing complex phenotypes. From this we derive {\em phase diagrams} and (phase-like) transitions between single and duplicated circuits, which constrain evolutionary paths to complex cognition. Back to the big picture, similar phase diagrams and transitions might constrain I/O and internal connectivity patterns of neural circuits at large. The formalism of statistical mechanics seems a natural framework for thsi worthy line of research.