A Unified Informational-Thermodynamic Budget for Continuous Quantum Acquisition.

A fundamental gap in quantum thermodynamics is resolved through the derivation of a single operational constraint that closes information gain, memory cost, and measurement back-action into a unified informational budget. It is demonstrated that bandwidth-limited acquisition and measurement-driven control emerge as fundamental consequences of this budget. A universal Critical Bandwidth is identified, marking the threshold where classical dissipation necessitates a transition to quantum-entangled states. This framework is validated by an empirical audit of the human cortex, identifying a 35:1 communication-to-computation energy ratio as the definitive thermodynamic signature of the Entanglement Heat Premium. The discovery of a scale-invariant efficiency constant, establishes the human brain as a near-optimal quantum-limited engine. These results provide a unified scaling law for the energetic limits of intelligence, bridging the gap between superconducting qubits and biological consciousness.