HYPOELLIPTIC ENTROPY DISSIPATION FOR STOCHASTIC DIFFERENTIAL EQUATIONS

Both the paper and the model use the same Γ2/Bochner-curvature method: (i) compute d/dt of the weighted Fisher information Ia,z via an information Γ2 identity, (ii) decompose Γ2 into a nonnegative squared Hessian term plus curvature tensors Ric + RicI, and (iii) invoke the pointwise curvature bound Ric + RicI ⪰ λ(aa^T + zz^T) to obtain dI/dt ≤ −2λ I and hence exponential decay. The entropy dissipation d/dt DKL = −Ia (with cancellation of the γ-term by ∇·(πγ)=0) is also identical. The only discrepancy is that the paper’s displayed L1 bound in Corollary 3(ii) omits a square root on the initial Fisher information, whereas the subsequent argument via Csiszár–Pinsker and the derived KL bound yields the correct form with √Ia,z(p0‖π). The model states this corrected inequality and is otherwise aligned. We therefore judge both correct in substance, noting a minor typographical/presentation issue in the paper and a small step in the model where the passage s→∞ relies on DKL(ps‖π)→0.