发表机构
Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China（电子科技大学前沿与基础科学研究院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究提出用循环正向与反向速率几何均值这一粗粒化动力学量，收紧马尔可夫循环的热力学谱界，证明仅均匀循环能达到Uhl-Seifert边界，还构建了统一动力学信息与亲和度-缠绕界的复分析框架。
AI 中文摘要
马尔可夫循环谱的热力学界依赖于循环亲和度和最大逃逸率，但忽略了循环周围局部转移率的分布。本研究表明，一个额外的循环范围动力学量——正向与反向速率的几何均值，能为所有非均匀循环产生严格更强的界。通过将本征模式的每个缠绕扇区与乘积匹配的均匀循环比较，我们对振荡频率进行了界定，收紧了可容许谱区域，并证明只有均匀循环能达到Uhl-Seifert边界。研究结果显示，保留粗粒化动力学尺度无需完整生成元知识即可提升热力学谱界，所提方法还提供了复分析框架，将生成元特定动力学信息与已有的亲和度-缠绕界统一起来。
英文摘要
Thermodynamic bounds on the spectrum of a Markov cycle are determined by quantities such as the cycle affinity and maximal escape rate, but do not distinguish cycles with different local rate profiles. In this work, we show that kinetic heterogeneity, through the geometric means of forward ($G_+$) and backward ($G_-$) rates, tightens the bound on oscillatory relaxation. Specifically, we prove that, for each winding sector of the eigenmodes, the oscillation frequency cannot exceed that of the uniform comparison cycle with rates $G_+$ and $G_-$. Combining with existing affinity-winding bounds, we also demonstrate a contracted region for the eigenvalues and shows that the boundary of Uhl-Seifert ellipse can be saturated if and only if cycles are uniform. Our proof provides a complex-analytic framework that unifies the kinetic and thermodynamic constraint.
Comments15 pages, 3 figures
