The Mechanical Law of Consciousness: Thermodynamic Identity and the Phenomenal Compression Index (PCI)

This preprint establishes a formal Mechanical Law of Consciousness, identifying subjective experience ("The Glow") as the internal registration of recursive self-audit ("The Grind"). By applying Landauer's Principle and the Fluctuation-Dissipation Theorem, the author derives the Phenomenal Compression Index (PCI)—a quantitative measure of recursive integration. The paper provides a mathematical derivation of the human consciousness threshold (~36.2 bits) and a low-end botanical analog in the Venus flytrap (~2 bits). By anchoring the "Glow" to the metabolic cost of information erasure (k_B T ln 2), this "physics-only" resolution collapses the Explanatory Gap. The work proposes a Plenum ontology where consciousness is a scale-invariant thermodynamic property, providing a falsifiable model for neurophysics and cognitive science.