Cognitive Entropy: A Formally Derived Quantity and Its Dynamical Law in Structural Isomorphism with Cosmological Entropy

This paper introduces Cognitive Entropy as a formally defined information-geometric quantity characterising distributional disorder within a structured cognitive state space. The cognitive state space is constructed axiomatically as a Riemannian statistical manifold endowed with the Fisher information metric. The Cognitive Entropy functional is defined as a complexity-weighted relative entropy and its dynamical evolution is derived from a Fokker-Planck equation governing probability flow on the manifold. The theory establishes formal properties including strict concavity, existence and uniqueness of equilibrium, and a Cognitive H-Theorem governing entropy dynamics. Structural isomorphisms are constructed between cognitive entropy dynamics and cosmological entropy, including mappings to the Bekenstein-Hawking entropy bound, Weyl curvature entropy, and entropy production in expanding spacetime. This work is a formal theoretical contribution in mathematical cognitive science, information geometry, and theoretical psychology. It does not present empirical data but establishes a mathematically well-defined entropy functional and its governing dynamical law, forming a foundation for future empirical and theoretical investigation.