Axiomatic Dissipative Agency: A Thermodynamic and Cybernetic Foundation for Embodied Autonomous Systems

Traditional autonomous architectures bifurcate cognitive task planning from homeostatic survival, arbitrating mission execution and metabolic replenishment through discrete heuristic thresholds or ungrounded scalar utility functions. This divide introduces systemic failure modes, including chattering hysteresis, boundary starvation, and suboptimal kinetic dissipation. This work introduces the Axiomatic Theory of Dissipative Agency, a foundational cybernetic framework that derives autonomous behavior directly from non-equilibrium thermodynamics and constitutive mass-action kinetics. By modeling an agent as an open, two-stock dissipative system—composed of structural biomass (B) and a liquid free-energy store (E)—this work establishes the following analytical foundations: 1. Master Equation of State: Internal metabolic throttle partitioning collapses identically into a universal scalar invariant (Pi = Xi), defining the admissible boundaries of the agent's viable continuation tube.2. Structural Observability Asymmetry: Under open-loop metabolic degradation, liquid energy (E) acts as a full state observer of structural biomass (B) through somatic maintenance coupling, whereas biomass cannot observe energy. Consequently, single-sensor scalar energy feedback is proven mathematically sufficient to asymptotically stabilize both internal stocks.3. Allosteric Control Barrier Functions (CBFs): Non-linear homeostatic urgency functions as a continuous Control Barrier Function, guaranteeing forward invariance of the viability kernel (K) and strictly preventing catastrophic starvation.4. Directional Metric Tensors: External kinetic dissipation is formalized as a state-dependent Riemannian metric tensor (Q), proving that biological momentum conservation is the natural pursuit of kinetic geodesics. These theoretical derivations are cross-validated against the published Biological Principle of Least Action (BPLA) benchmark dataset (DOI: 10.5281/zenodo.19237175). The analysis demonstrates that empirical phenomena reported in embodied least-action navigation—including an 86.9% momentum utilization rate, complete elimination of near-death starvation (0.0% vs. 6.2%), parsimonious environmental key interactions (6 vs. 25 activations), and rapid convergence to an invariant 58-tick limit cycle—are direct, necessary mathematical consequences of dissipative agency. This deposit contains the full theoretical manuscript, mathematical proofs (including Jacobian stability, observability rank conditions, and CBF forward invariance), and comparative benchmark evaluations.