Temporal Infomax Leads to Almost Deterministic Dynamical Systems

The well-known Kullback-Leibler divergence of a random field from its factorization quantifies spatial interdependencies of the corresponding stochastic elements. In the present work, we introduce a generalized measure for stochastic interaction that captures also temporal interdependencies. Maximization of stochastic interaction in the setting of Markov chains is shown analytically and by simulations to result in an almost deterministic global dynamics, but, simultaneously, almost unpredictable single unit activity