Multiscale Coordination of Dissipative Systems: Coupling Metabolic Allocation with Algebraic Orthant Constraints

Abstract:The persistent survival of biological systems in non-stationary, resource-constrained environments depends on coupling thermodynamic stability, metabolic allocation, and regulatory consistency across multiple scales. This paper introduces a formal framework that couples a state-space formulation of metabolic reserve dynamics with algebraic constraints on actuator coordination, yielding the Coupled Persistence System (CPS). By modeling the system's viability zone as a bounded manifold, we derive a coupled dynamical system that relates viability margins directly to energy mobilization. To prevent mutually destructive actuator commands across different hierarchical levels, we introduce a Constrained Orthant Lattice (COL) that enforces algebraic mutual exclusion on opposing action vectors. Under this formulation, the state trajectories are governed by a modified gradient flow of an augmented potential, modulated by a scaling tensor. In a simulated six-dimensional dynamical environment subject to sensory latency and resource volatility, this coupled formulation exhibits improved energetic efficiency compared to standard baseline active inference models, specifically by reducing high-frequency actuator oscillations ("metabolic jitter"). These results suggest that algebraic constraints on physical action space complement predictive, informational optimization in robust biological control. Note: This preprint is prepared for submission to Peer Community In (PCI) Mathematical and Computational Biology.