重大事件与生物学

P. Grigolini
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引用次数: 0

摘要

在20世纪的最后几年,从事统计物理的物理学家的注意力从以平稳相关函数和泊松动力学为特征的平衡过程转移到具有遍历性断裂的生物过程。这些过程的发现引发了一场争论,即像昂萨格原理这样的基本性质是应该放弃还是应该适当地重新审视。利维过程的发现使许多研究者用广义中心极限定理取代了传统的中心极限定理,这与普通的高斯统计有了显著的不同。自组织过程的发现使得对雪崩的研究变得非常流行。2 .对湍流过程的观察发现了新的等待时间分布密度,其特征为逆幂定律3,并且发明了一个新的随机中心极限定理来解释mittagg - leffler函数的出现,该函数现在被广泛用于分数阶导数的基础。4 . Kubo的传统线性响应理论被一种新的线性响应形式所取代,这种新的线性响应形式与复杂系统的遍历击穿相适应,并以此作为复杂性匹配(CM)的基础。我打算证明关键事件是导致遍历性破缺的原因,CM现象是关键事件的一种表现。在这一研究领域仍然存在的一个问题是[公式:见文本]噪声的起源,噪声传统上被解释为曼德尔布罗特分数布朗运动(FBM)的表现。6 .我打算表明,在5中提出的CM现象基础的噪声具有完全不同的性质,涉及关键事件,而不是FBM无限记忆。我的研究小组7最近的一项结果证明,自主神经病变的进展使健康个体的心跳由关键事件主导,变成FBM。令人惊讶的是,在没有光的情况下,小扁豆的萌发过程中也观察到同样的从关键事件到FBM状态的过渡现象。从利维统计到高斯统计的转变应该是由环境波动产生的,我将举例说明实验和理论研究工作,这些工作将阐明它们的本质。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Crucial Events and Biology
In the last years of the 20th century, the attention of physicists working in statistical physics moved from equilibrium processes characterized by stationary correlation functions and Poisson dynamics to biological processes exhibiting ergodicity breaking. The discovery of these processes raised a debate on whether basic properties such as the Onsager principle had to be abandoned or properly revisited. 1 The discovery of Levy processes led many researchers to replace the conventional central limit theorem with the generalized central limit theorem, responsible for a striking departure from the ordinary Gaussian statistics. The discovery of the processes of self-organization made the study of avalanches become very popular. 2 The observation of turbulent processes led to the discovery of new waiting time distribution densities, characterized by inverse power laws 3 and a new stochastic central limit theorem was invented to explain the emergence of Mittag-Leffler function, which is now widely used for the foundation of fractional derivatives. 4 The traditional Linear Response Theory of Kubo was replaced by a new form of linear response, compatible with the ergodic breakdown of complex systems, and this new form of linear response was used for the foundation of Complexity Matching (CM). 5 I plan to prove that crucial events are responsible for ergodicity breaking and that the CM phenomenon is a manifestation of crucial events. One problem still open in this field of research is the origin of [Formula: see text] noise that is traditionally interpreted as a manifestation of the Mandelbrot Fractional Brownian Motion (FBM). 6 I plan to show that the [Formula: see text] noise proposed in 5 for the foundation of the CM phenomenon has a completely different nature, involving crucial events rather than the FBM infinite memory. A recent result of my research group 7 proved that the progress of autonomic neuropathy makes the heartbeats of healthy individuals, dominated by crucial events, turn into FBM. Quite surprisingly, the same phenomenon of transition from the crucial event to the FBM regime was observed in the germination process of lentils 8 in the absence of light. The transition from Levy to Gauss statistics is supposed to be generated by environmental fluctuations and I will illustrate the experimental and theoretical research works that will shed light into their nature.
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