Macroscopic Order Formation, Inflation Mechanism and Entropy Change(Nonequilibrium Dynamics in Astrophysics and Materials Science)

概要

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In 1976, the author developed the scaling theory of order formation from unstable states by extending Einstein's linear theory of Brownian motion to nonlinear unstable cases. At the first stage, an exponential growing has been shown to be dominant, namely the initial microscopic fluctuation grows rapidly upto the macroscopic order around the onset time in the scaling regime, where the nonlinearity of the relevant system plays an essential role to stabilize the system. The author found the synergetic effect (or synergism) of the initial fluctuation, random noise and nonlinearity to the formation of macroscopic order. This scaling theory of a single macrovariable or order parameter has been extended to an infinite number of order parameters. The entropy change or entropy production is also discussed from a new point of view, namely from the symmetry of the non-equilibrium density-matrix, using the von Neumann equation. The time derivative of the entropy production for general transport phenomena is also given and consequently this formula yields microscopically the principle of minimum entropy production in the linear response scheme of transport phenomena. Furthermore, we propose here a new principle of minimum dissipation for nonlinear transport phenomena such as nonlinear electric circuits whose resistances depend on currents.
理論物理学刊行会の論文
2012-08-08