A central challenge in quantum physics is to understand the structural properties of many-body systems, both in equilibrium and out of equilibrium. For classical systems, we have a unified perspective which connects structural properties of systems at thermal equilibrium to the Markov chain dynamics that mix to them. We lack such a perspective for quantum systems: there is no framework to translate the quantitative convergence of the Markovian evolution into strong structural consequences. We develop a general framework that brings the breadth and flexibility of the classical theory to quantum Gibbs states at high temperature. At its core is a natural quantum analog of a Dobrushin condition; whenever this condition holds, a concise path-coupling argument proves rapid mixing for the corresponding Markovian evolution. The same machinery bridges dynamic and structural properties: rapid mixing yields exponential decay of conditional mutual information (CMI) without restrictions on the size of the probed subsystems, resolving a central question in the theory of open quantum systems. Our key technical insight is an optimal transport viewpoint which couples quantum dynamics to a linear differential equation, enabling precise control over how local deviations from equilibrium propagate to distant sites.

翻译：量子物理学的一个核心挑战是理解多体系统的结构性质，无论是在平衡态还是非平衡态。对于经典系统，我们拥有一个统一的视角，将热平衡下系统的结构性质与混合至该平衡的马尔可夫链动力学联系起来。对于量子系统，我们缺乏这样的视角：目前没有框架能将马尔可夫演化的定量收敛转化为强有力的结构推论。我们开发了一个通用框架，将经典理论的广度和灵活性引入高温下的量子吉布斯态。其核心是一个自然的 Dobrushin 条件的量子类比；只要该条件成立，一个简洁的路径耦合论证即可证明相应马尔可夫演化的快速混合。同样的机制连接了动力学与结构性质：快速混合导致条件互信息（CMI）的指数衰减，且对被探测子系统的大小没有限制，从而解决了开放量子系统理论中的一个核心问题。我们关键的技术见解是最优输运的视角，它将量子动力学与一个线性微分方程耦合起来，从而能够精确控制局部偏离平衡如何传播到远处位点。