Regression law of fluctuations and self-similarity law near critical point by noting a hierarchical structure of nature

In the case of a system far from equilibrium including a bifurcation point, the conventional perturbation theory becomes irrelevant. Fluctuations near critical point give rise to a macroscopic effect and behave nonlinearly. So-called an asymptotic method for analysis of such large fluctuations occurring, for example, in chemical systems is proposed, in which case, it is basic that dynamics is described by a master equation. Here, we present the master equation written by a newly defined generating function. By noting a hierarchical structure of nature and introducing new moment generating functions with a scaling expansion method, we can show that the macroscopic transport law, the equation of motion describing the fluctuating deviations from the deterministic path and the equation of the variance of fluctuation is automatically obtained. It is also shown that even at such a near critical point the hypothesis called the regression law of fluctuations is still valid.