Oxford paper mathematically bridges IIT and Free Energy Principle for consciousness

The Free Energy Principle (FEP) and Integrated Information Theory (IIT) are two dominant but mathematically distinct frameworks for understanding self-organization and consciousness. Alexander Kearney's Oxford thesis (84 pages, 10 figures) provides the first rigorous mapping between them by redefining information as the deviation ψ of realized dynamics from a constrained maximum-caliber (MaxCal) path ensemble over finite time. Under this definition, IIT 3.0's central cause/effect repertoires emerge directly from MaxCal variational principles, effectively rederiving IIT's phenomenological calculus from constrained entropy maximization (CMEP). This supplies a theoretical bridge to active inference, which Kearney shows is mathematically dual to CMEP under Langevin dynamics.

When applied to Markov chains and Ising models via large deviations theory, ψ becomes equivalent to prediction error under predictive coding models. This resolves the 'hill-shaped trajectory' of Φ (IIT's measure of integrated information) observed in neuronal cultures adapting to sensory inputs. The work grounds consciousness in violations of the Fluctuation-Dissipation Theorem, tying together thermodynamics, cognition, and neural dynamics. For AI researchers, this offers a principled path to designing systems that combine self-organization (FEP) with causal structure (IIT), potentially leading to more robust and conscious-like artificial agents.