可逆马尔可夫动力学中弛豫与第一次通过之间的对偶性：解开的崎岖能量图景
Duality Between Relaxation and First Passage in Reversible Markov Dynamics: Rugged Energy Landscapes Disentangled
摘要：
弛豫和第一通道过程是凝聚态、聚合物和单分子体系动力学的支柱。然而，到目前为止，弛豫和首次通过时间尺度之间的明确联系仍然难以捉摸。在这里，我们证明了它们之间的对偶性的形式交错的频谱。在基本形式中，对偶性对于有效一维目标的可逆马尔可夫过程成立。三阱势的探索进行了分析，以展示如何的二元性允许一个直观的理解第一通道轨迹的弛豫本征模。更一般地说，我们提供了一个全面的解释，在崎岖的潜力，包括反应轨迹的全部统计。即所谓的“很少遭遇限制”。我们的研究结果是定量解释蛋白质错误折叠引发的疾病的发生所必需的。
英文摘要：
Relaxation and first passage processes are the pillars of kinetics in condensed matter, polymeric and single-molecule systems. Yet, an explicit connection between relaxation and first passage time-scales so far remained elusive. Here we prove a duality between them in the form of an interlacing of spectra. In the basic form the duality holds for reversible Markov processes to effectively one-dimensional targets. The exploration of a triple-well potential is analyzed to demonstrate how the duality allows for an intuitive understanding of first passage trajectories in terms of relaxational eigenmodes. More generally, we provide a comprehensive explanation of the full statistics of reactive trajectories in rugged potentials, incl. the so-called `few-encounter limit'. Our results are required for explaining quantitatively the occurrence of diseases triggered by protein misfolding.
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