Scaling Theory of Transient Nonlinear Fluctuations and Formation of Macroscopic Order
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概要
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This paper constitutes partially a review of the essence of a series of papers published by the present author concerning the statistical mechanics of nonequilibrium systems and the scaling theory of transient phenomena near the instability point. That is, the extensivity or existence of thermodynamic limit of non-equilibrium systems is proven under quite general conditions. This yields the anomalous fluctuation theorem that the variance around the most probable path shows an anomalous enhancement of fluctuation inversely proportional to the square of the deviation δ of the initial system from the instability point, in the extensive region (i. e., δ^21≫ε≡Q^<-1>;Q is the system size). In the unstable region (δ^2 gsim ε), a new asymptotic evaluation method, that is, the scaling theory is very useful to describe nonlinear fluctuations and formation of macroscopic order. This scaling theory gives the fluctuation-enhance-ment theorem, i. e., macroscopic enhancement of fluctuation from the initial microscopic one. This is the essential mechanism of the onset of macroscopic order or structure, including dissipative structure. Conceptually, this scaling theory yields the importance of synergism (or cooperative effect) of initial fluctuations, random force and nonlinearity of the system for the onset of macroscopic order. The scaling theory of nonlinear Brownian motion is also formulated. A new systematic global approach to nonlinear Brownian motion is proposed as well as a simple dynamic molecular field treatment of it.
- 理論物理学刊行会の論文
- 1979-04-01
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