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The Fenchel Game of Underdamped Langevin Dynamics: Insights into Accelerated Convergence
For $(Q_t,P_t)$ governed by suitably damped underdamped Langevin dynamics, we quantify the convergence in KL divergence of the positional marginal to a $σ$-strongly log-concave target $π(dq) = \frac{1}{Z}e^{-V(q)}dq$ as \begin{align*} \operatorname{KL}(\operatorname{Law}(Q_t) \| π) \leq e^{-\sqrtσ t
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