Chemical Viscosity in U-shape and Conserved H-theorem: Reactive Boltzmann Model with B_{12} >= 0 and Arrhenius Derivation

This work addresses the classical limitation of the Boltzmann model where the cross-section B = d^2 yields a monotonic viscosity mu ~ sqrt(T) without U-shaped behavior.

The Bolyblev model B = B1 + B2 < 0 reproduces a U-shape but violates the H-theorem (dH/dt <= 0).

We introduce a corrected reactive cross-section:

B_{12} = d^2 + A_2 exp(-E_a / kT) |b| >= 0

with C^infinity angular cutoff, bounded and non-negative. The reaction frequency nu_{12}(T) is derived exactly via Bessel K2 function leading to nu ~ exp(-E_a / RT).

The resulting chemical viscosity is mu_chem = kT / nu_reac, exhibiting a unique minimum at T* = E_a / (R * 1.618), vulgarized as RT* = E_a. The model conserves the H-theorem, respects Grad cutoff and admits DiPerna-Lions renormalized solutions.