Trachenko-Zaccone方程：从玻璃态到复杂系统的非线性弛豫
The Trachenko-Zaccone equation: nonlinear relaxation from glasses to complex systems
AI总结：
本综述介绍Trachenko-Zaccone方程的概念发展、物理起源、数学结构、应用场景及未来方向，指出其可作为通用非线性反馈方程应用于复杂系统。
AI中文摘要：
Trachenko-Zaccone方程为描述无序凝聚态物质中的非德拜弛豫提供了一个紧凑的非线性动力学框架。该方程最初是为了从相互作用局域弛豫事件的动力学出发，合理化液体和玻璃态中的拉伸及压缩指数弛豫而开发的，随后它也出现在更广泛的场景中，包括聚合物弛豫和全局种群动力学的非线性模型。本综述追溯了该方程的概念发展，特别强调了它在Kostya Trachenko提出的前馈相互作用机制中的物理起源、数学结构及其可能的推广形式。我们还包含了2019年8月在伦敦玛丽女王大学与Kostya Trachenko合作的个人回忆，当时该方程基本以目前的形式被提出。在综述了其在应力弛豫、玻璃态材料、聚合物弛豫和种群动力学中的应用后，我们讨论了未来的研究方向，包括时变反馈参数、耦合序参量、非均匀及空间分辨的公式、通量项、网络版本和随机扩展。本综述的核心主题是，Trachenko-Zaccone方程不仅应被视为玻璃态弛豫的模型，还应被视为具有跨复杂系统应用潜力的通用非线性反馈方程。
英文摘要：
The Trachenko-Zaccone equation provides a compact nonlinear dynamical framework for describing non-Debye relaxation in disordered condensed matter. Originally developed to rationalize stretched- and compressed-exponential relaxation in liquids and glasses from the dynamics of interacting local relaxation events, the same equation has subsequently appeared in broader contexts, including polymer relaxation and nonlinear models of global population dynamics. This review retraces the conceptual development of the equation, with particular emphasis on its physical origin in Kostya Trachenko's feed-forward interaction mechanism, its mathematical structure, and its possible generalizations. We also include personal recollections of the work with Kostya Trachenko at Queen Mary University of London in August 2019, during which the equation emerged in essentially its present form. After reviewing applications to stress relaxation, glassy materials, polymer relaxation and population dynamics, we discuss future directions including time-dependent feedback parameters, coupled order parameters, heterogeneous and spatially resolved formulations, flux terms, network versions and stochastic extensions. The central theme of the review is that the Trachenko-Zaccone equation should be viewed not only as a model of glassy relaxation, but as a general nonlinear feedback equation with potential applications across complex systems.
