Rotational Coherence Collapse at the Mitochondrial Scale: A Statistical Physics Framework for the Warburg Phase Transition in Cellular Oncogenesis

We present a statistical physics framework describing the transition of mitochondrial rotary motors from a coherent high-energy state to an incoherent low-energy state, and identify the geometric threshold governing this transition. The ATP synthase — a rotary molecular motor operating at 100–150 revolutions per second (RPS) [1,2] — is modelled as an active biological oscillator whose coherence is parametrised by the Axial Coherence Factor (ACF). The critical threshold ACF = 0.65 is derived from first principles by the present work by combining two independent physical constants: the three-dimensional random close-packing percolation threshold (pc = 0.4120 [3,4]) and the Jacobi ellipsoid rotational stability limit (Rmin = 2/3 [5]), yielding ACF = (pc × Rmin)^(1/3) = 0.650033 (deviation 0.0051% from the empirically identified value; z = 0.013σ) [6]. Below this threshold, the system undergoes a deterministic phase transition: rotational coherence collapses, oxidative phosphorylation fails, and the cell activates compensatory aerobic glycolysis — the Warburg effect [7]. The cell membrane potential simultaneously depolarises from −70 mV (coherent, creation mode) to −15 to −30 mV (collapsed, maintenance mode) [8,9], providing a directly measurable macroscopic correlate of the microscopic phase transition. This framework positions cancer as a physical phase transition in a dissipative active matter system rather than a stochastic accumulation of genetic errors. Statistical validation using Fisher's method (df-corrected, df = 38) across 19 independent empirical domains yields χ² = 172.59, p = 4.61×10⁻¹⁹, σ = 8.84. Critically, the three biological physics domains alone — excluding all prior theoretical series — yield σ = 5.16 (χ² = 42.83, df = 6, p = 1.26×10⁻⁷), confirming that the empirical evidence independently crosses the 5σ discovery threshold. Three falsifiable predictions are presented for experimental validation. Medical Disclaimer. This manuscript is a theoretical biophysics paper applying statistical physics to published peer-reviewed biological data. The content does not constitute medical advice, clinical diagnosis, or therapeutic guidance. No decisions regarding treatment, medication, or health protocols should be made based on this work without the direct supervision of a qualified physician. The diseases discussed are serious medical conditions requiring professional clinical management.