Non-Equilibrium Quantum Thermodynamics of Nuclear Fusion: Resource-Theoretic Bounds, Fluctuation Theorems, and Thermodynamic Uncertainty Relations for Plasma Ignition

Fusion plasma physics and quantum thermodynamics have developed over several decades as mature but essentially disconnected disciplines, with virtually no cross-citations linking the two literatures. We bridge this gap by establishing the first unified theoretical framework — Non-Equilibrium Quantum Thermodynamics of Fusion (NEQT-Fusion) — and prove four theorems that impose new, fundamental constraints on fusion plasma ignition and power balance. Theorem 1 (Resource-Theoretic Lawson Criterion). We reformulate ignition as a state-conversion problem in the resource theory of thermodynamics. A family of generalized free-energy conditions, F_α (ρ)≥F_α (ρ_ign ) for all Rényi orders α≥0, is shown to be necessary for ignition. These conditions reduce to the classical Lawson triple-product criterion in the macroscopic Maxwellian limit but provide strictly stronger constraints for non-Maxwellian plasmas. We construct an explicit proton–boron-11 (p-^11B) counterexample in which the classical Lawson criterion is satisfied yet a higher-order Rényi condition (α=∞) is violated, rendering ignition thermodynamically forbidden. Theorem 2 (Quantum Crooks Relation for Fusion Reactivity). The ratio of forward (fusion) to reverse (disassembly) stochastic work distributions for plasma-screened Coulomb tunneling satisfies the exact quantum Crooks fluctuation theorem, P_F (W)/P_R (-W)=exp[β(W-ΔF)]. This yields a thermodynamic ceiling on non-Maxwellian reactivity enhancement via the Jarzynski equality and motivates new, model-independent diagnostics: the Crooks asymmetry curvature κ_R as a non-equilibrium indicator and the Jarzynski-extracted athermality from neutron time-of-flight spectra in NIF-class burning plasmas. Theorem 3 (TUR Bound on Recirculating Power). The precision of maintaining a non-Maxwellian ion distribution against collisional relaxation is bounded by total entropy production through the thermodynamic uncertainty relation, Var(P_rec )/⟨P_rec ⟩^2≥2k_B/S ̇_tot. In the quantum-degenerate electron regime, this bound is sharpened, reinforcing the energetic impossibility of steady-state aneutronic fusion via a precision–dissipation tradeoff absent from classical analyses. Theorem 4 (Unified NEQT-Fusion Criterion). The preceding three results are combined into a single master inequality governing the net engineering gain Q_eng, subject to the simultaneous satisfaction of all generalized free-energy conditions, the reactivity ceiling, and the TUR power-balance constraint. The framework subsumes the Lawson criterion (1957) and Rider’s recirculating-power bound (1997) as limiting cases, while furnishing strictly new constraints in non-Maxwellian, mesoscopic, and quantum-degenerate regimes. It thereby establishes NEQT-Fusion as a new interdisciplinary research direction at the intersection of quantum information science and fusion energy science.