A statistical mechanical problem?

Tommaso Costa, Mario Ferraro

The problem of deriving the processes of perception and cognition or the modes of behavior from states of the brain appears to be unsolvable in view of the huge numbers of elements involved. However, neural activities are not random, nor independent, but constrained to form spatio-temporal patterns, and thanks to these restrictions, which in turn are due to connections among neurons, the problem can at least be approached. The situation is similar to what happens in large physical ensembles, where global behaviors are derived by microscopic properties. Despite the obvious differences between neural and physical systems a statistical mechanics approach is almost inescapable, since dynamics of the brain as a whole are clearly determined by the outputs of single neurons. In this paper it will be shown how, starting from very simple systems, connectivity engenders levels of increasing complexity in the functions of the brain depending on specific constraints. Correspondingly levels of explanations must take into account the fundamental role of constraints and assign at each level proper model structures and variables, that, on one hand, emerge from outputs of the lower levels, and yet are specific, in that they ignore irrelevant details.