Crucial Events and Biology

Abstract

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.