超统计制度之间的转变：有效性，分解和应用
Transitions between superstatistical regimes: validity, breakdown and applications
摘要：
超统计是非平衡态统计物理的一个广泛应用的工具，在分析递阶复杂动力系统中起着重要的作用。然而，它的“规范”制定在一个单一的滋扰参数往往是过于限制性的，当应用于复杂的经验数据。在这里，我们表明，超统计范式的多尺度泛化是更通用的，允许解决统计或尺度间随机行为的嬗变等相关问题。为了让这些数据更真实，我们通过分析七家选定公司的股价回报率高频（分钟刻度）数据，为两种超级统计制度之间的过渡提供了数字证据。突出的问题，如分数扩散过程中的超统计量的故障或布朗从属连接也进行了简要讨论。
英文摘要：
Superstatistics is a widely employed tool of non-equilibrium statistical physics which plays an important role in analysis of hierarchical complex dynamical systems. Yet, its "canonical" formulation in terms of a single nuisance parameter is often too restrictive when applied to complex empirical data. Here we show that a multi-scale generalization of the superstatistics paradigm is more versatile, allowing to address such pertinent issues as transmutation of statistics or inter-scale stochastic behavior. To put some flesh on the bare bones, we provide a numerical evidence for a transition between two superstatistics regimes, by analyzing high-frequency (minute-tick) data for share-price returns of seven selected companies. Salient issues, such as breakdown of superstatistics in fractional diffusion processes or connection with Brownian subordination are also briefly discussed.
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