Entropy Accounting, Energy Budgets, and the Second Law in Radial Coherential Dynamics

This paper provides the thermodynamic closure of the Radial Coherential Dynamics (RCD) program (Papers XIV-A to XIV-E). A critical audit identified a fundamental gap: if coherence is protected by a dynamical mechanism, where does the entropy of filtered noise go? Without explicit accounting, such protection risks violating the Second Law of Thermodynamics. We show that coherence protection in RCD is not thermodynamically free. It requires continuous energy expenditure and entropy export to identifiable baths. Using Landauer’s principle and quantum thermodynamic bounds, we derive the minimum energetic cost of coherence maintenance and demonstrate that the universal ratio α ≡ Γ/J emerges as an efficiency parameter constrained by irreversibility, not as a fundamental constant. The N-signatures (memory, protection, emergent scale) are mapped onto concrete thermodynamic resources: mutual information, entropy valves, and temperature differentials. Domain-specific realizations are discussed for superconducting qubits, cosmological dark energy dynamics, and neural systems. The C-field is shown to function as a Maxwell-type demon that fully pays its thermodynamic debt. The Second Law is satisfied at all scales. This work completes the logical and physical closure of the RCD XIV series.