Universal Dynamic Balance: A Unified Variational Framework for Physical, Biological, and Informational Systems

We propose the Theory of Universal Dynamic Balance (UDB), a unifying variational framework describing the evolution of systems across physical, biological, and information-driven domains. UDB generalizes non-equilibrium thermodynamic principles and field-theoretic gradient-flow dynamics by introducing a generalized imbalance functional F[q] defined on a rigorously specified configuration manifold, whose minimization governs system stability. Stability is characterized by a positive-definite Hessian H[F] in the appropriate functional space. Information structure enters through the von Neumann entropy S_vN = -Tr(ρ ln ρ) or, in classical stochastic settings, the Shannon entropy H = -Σ p_i ln p_i, with a precisely defined coupling coefficient λ_Φ. We derive quantitative predictions for Bose-Einstein condensates (BEC) via correspondence with the Gross-Pitaevskii functional, for homeostatic regulation via Lyapunov stability analysis, and for collective phase transitions in coupled network dynamics. UDB is explicitly positioned relative to Friston's free energy principle, Prigogine's non-equilibrium thermodynamics, and Haken's synergetics, identifying its distinguishing contributions. Testable predictions include a modified critical atom number for BEC collapse and a critical coupling threshold for opinion consensus in social networks.