Homeothermic Immunothermodynamics versus Cryogenic Superconductivity: Febrile Leukocyte Activation (37 C-40 C), Intracellular Ice-Ih Membrane Rupture and Hypothermic Ventricular Fibrillation (< 30 C), Targeted Temperature Management (TTM), and Non-Equilibrium Vibronic Life

A profound thermodynamic dichotomy separates inanimate solid-state quantum matter from living biological organisms. Whereas metallic and cuprate superconductors require deep cryogenic cooling in liquid nitrogen (T_LN2 = 77 K = -196 C) or liquid helium (T_LHe = 4.2 K = -269 C; 15 mK in dilution refrigerators) to suppress thermal phonon scattering and sustain zero-resistance Cooper-pair condensates, homeothermic mammals maintain a tightly regulated core temperature around T_core ≈ 310.15 K (37.0 C). Subjecting a water-rich biological organism to cryogenic cooling does not induce biological superconductivity; instead, it triggers lethal cellular perforation and electrophysiological arrest. Conversely, when challenged by bacterial or viral invasion, the mammalian immune system intentionally elevates core temperature into the febrile regime (38 C-40 C), while clinical medicine utilizes strictly bounded mild hypothermia (Targeted Temperature Management [TTM], 33 C-36 C) only as a controlled metabolic brake following cardiac resuscitation. Building upon our prior CERN Zenodo monographs on room-temperature biomimetic phononic coherence (Record 23333819), 300 K polaronic quantum spiking networks (Record 23334854), and Super-RTO nanodiamond Sobolev-HOCBF clinical interlocks (Record 23377123), this monograph establishes the unified mathematical biophysics of Homeothermic Immunothermodynamics. We prove four core theorems: (1) Bifurcated Eyring-Arrhenius Febrile Defense (37 C -> 39.5 C): Pyrogenic elevation of T_core exponentially accelerates leukocyte chemotaxis, CD8+ T-cell proliferation, and antibody synthesis (+45% to +110%) while driving viral/bacterial replication enzymes across their thermal denaturation cliff (T > T_opt ≈ 37 C), flipping the Lotka-Volterra infection eigenvalue negative; (2) Dendritic Ice-Ih Nucleation & Lipid-Bilayer Perforation (< 0 C): Because hexagonal ice-Ih expands by +9.05% upon freezing, intracellular ice dendrites generate mechanical stresses (σ_ice ≈ 805 MPa >> σ_rupture ≈ 4 MPa) that irreversibly shred cell membranes and capillaries; (3) Arrhenius Ion-Channel Dispersion & Ventricular Fibrillation (< 30 C): Below 35 C, enzymatic Q10 decay slows metabolism; below 30 C, differential Q10 scaling across cardiac I_Na, I_to (Osborne J-waves), and I_Ca,L channels induces transmural dispersion and lethal spiral-wave ventricular fibrillation; and (4) Sobolev-HOCBF Neuroprotective TTM Control (33 C-36 C): Using ultrasmall nanodiamond (USND) NV- quantum thermometry, we bound post-ROSC cerebral cooling within [33 C, 36 C] to suppress cerebral oxygen demand (CMRO2, -27.1% at 33 C) with zero arrhythmic risk. License & Integrity Covenant: Creative Commons Attribution 4.0 International (CC BY 4.0) with Strict No-Learn Covenant (NLL-v1.0-2026).