Gradient-Driven Balance and Feedback: A Unified Framework Linking Thermodynamics, Information Theory, and Adaptive Systems

Abstract We propose a unified balance-feedback framework describing physical and cognitive systems as gradient-driven dynamical processes. Heat is interpreted as a manifestation of energy imbalance, while Shannon entropy quantifies distributional spread across microstates. A general gradient-descent evolution equation is introduced, formally analyzed via a Lyapunov stability proof, and validated through agent-based simulation (N = 100 nodes, 300 iterations). Simulation results confirm monotonic decay of the imbalance functional Φ (x) by more than four orders of magnitude, rapid variance collapse, and robustness across stochastic noise levels σ ∈ 0. 00, 0. 05, 0. 15, 0. 30. The framework is extended to adaptive decision systems, offering a non-teleological interpretation of goal-directed behavior as gradient minimization under cognitive and environmental constraints. Connections are drawn to Prigogine's dissipative structures, Friston's free energy principle, and Haken's synergetics, establishing the framework within the broader landscape of self-organizing systems theory. Grounded in the Universal Balance-Feedback Framework (UBFF) and Four Universal Laws developed by the author over four decades of independent research, this work offers a mathematically rigorous and empirically testable foundation for cross-domain systems science.