Information as Maximum-Caliber Deviation: A bridge between Integrated Information Theory and the Free Energy Principle
arXiv Preprint Archive May 3, 2026 Alexander Kearney
Information can be defined as the deviation of realized dynamics from a constrained maximum-caliber path ensemble over a finite time horizon. Under this definition, the cause/effect repertoires central to Integrated Information Theory 3.0 emerge directly from maximum-caliber variational principles, allowing IIT's phenomenological calculus to be re-derived from constrained entropy-maximization. This framework provides a theoretical bridge to active inference, which is mathematically dual to this approach under Langevin dynamics. When applied via the Central Limit Theorem for Markov chains and large deviations theory to Ising models, this information measure is equivalent to prediction error under accompanying predictive coding models, potentially explaining the hill-shaped trajectory of Φ observed in neuronal cultures adapting to sensory inputs.