Generator–Filter Theory: Toward a Unified Framework of Energy–Information Dynamics

Generator–Filter Theory (GFT) proposes a conceptual framework for describing the universal dynamics of complex systems through the interplay of generative and constraining processes. It unifies perspectives from algebra, topology, thermodynamics, and category theory by representing systems as dual components: Generators (G) that produce variation, energy, or structure, and Filters (F) that impose coherence, selection, or information. Their interaction is quantified by the dimensionless ratio P = G/F, which measures the curvature of the energy–information landscape—a diagnostic of balance, stability, and emergent behavior. While the mathematical formalization of GFT remains in its conceptual stage, the framework anticipates a future formulation within a categorical topos, linking local algebraic generation with global topological filtration via adjoint functors. GFT provides a transdisciplinary language bridging physics, biology, and computation, positioning emergence as a manifestation of geometric curvature in energy–information space.