Statistical Mechanics of General Brownian Motions Underlying Irreversible Processes
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概要
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A statistical mechanical theory of general Brownian motions hidden at the bottom of irreversible processes, especially of "linear dissipative processes" is outlined. Postulating that macroscopic observations are gross, i.e., that the macroscopic behavior of a large system is specified with a very small number of macro-observables and that their observed values are given by suitable time averages, it is concluded that macro-observables are approximately one-valued integrals of motion in M.S. Green's sense (Sec.2) and that they have finite mutual correlations (Sec. 4). On the basis of these results we attempt to reformulate the equation of motion in classical mechanics (Liouville's equation) in terms of the observed values of macro-observables. In order to do this, a macroscopic counterpart of the phase space and that of a distribution function in it are introduced (Sec. 3). Next the secular motion of the macroscopic distribution function is calculated. In this way the general Brownian motions underlying irreversible processes are disclosed and their equation of motion is obtained: a Fokker-Planck equation (Sec. 4, 5) This equation is seen to agree exactly with that recently given by M. S. Green, who studied the present problem from the microscopic point of view as well, but in his case, because of some serious assumptions employed, it was no longer necessary to refer to the equation of motion in mechanics. Finally some discussions are given on the origin of the "Markoffian character" of the macroscopic motion and on the relation of the present theory to Hashitsume's semi-phenomenological one (Sec. 6).
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著者
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Yamamoto Tsunenobu
Chemistry Department Faculty Of Science Kyoto University
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YAMAMOTO Tsunenobu
Chemistry Department, Faculty of Science, Kyoto University