We formulate a new information-theoretic principle--the shifted composition rule--which bounds the divergence (e.g., Kullback-Leibler or R\'enyi) between the laws of two stochastic processes via the introduction of auxiliary shifts. In this paper, we apply this principle to prove reverse transport inequalities for diffusions which, by duality, imply F.-Y. Wang's celebrated dimension-free Harnack inequalities. Our approach bridges continuous-time coupling methods from geometric analysis with the discrete-time shifted divergence technique from differential privacy and sampling. It also naturally gives rise to (1) an alternative continuous-time coupling method based on optimal transport, which bypasses Girsanov transformations, (2) functional inequalities for discrete-time processes, and (3) a family of "reverse" Harnack inequalities.

翻译：我们提出了一种新的信息论原理——移位复合规则——该规则通过引入辅助移位来约束两个随机过程分布之间的散度（例如，Kullback-Leibler散度或Rényi散度）。在本文中，我们应用这一原理证明扩散过程的逆向输运不等式，通过对偶性，这些不等式蕴含了F.-Y. Wang著名的无维数Harnack不等式。我们的方法将几何分析中的连续时间耦合技术与差分隐私和抽样领域的离散时间移位散度技术相连接。同时，它自然地导出了：（1）一种基于最优输运的替代连续时间耦合方法，该方法绕过了Girsanov变换；（2）离散时间过程的泛函不等式；（3）一族“逆向”Harnack不等式。