A Statistical Theory of Linear Dissipative Systems, II

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Abstract
The statistical theory based on the probability of a given succesion of non-equilibrium states of a linear dissipative systems given by Onsager and Machlup is proved by direct calculation to be equivalent to the theory of Brownian motion discussed by Wang and Uhlenbeck based on the Fourier series method of Rice. A function, which determines the above-mentioned probability and is constructed from the dissipation functions and the rate of entropy production, is shown to increase on the average with the lapse of time and remain constant (i.e., have the minimum value zero) when and only when the system obeys the phenomenological linear relations given by the thermodynamics of irreversible processes. This theorem is an extension of the second law of thermodynamics. When the system is characterized by a single relaxation time, the expression of the above-mentioned probability is a little simplified. The method os fluctuating distribution function is developed. When it is applied to the theory of the shape of collision broadened spectral line, the new strong collision treatment proposed by Gross is proved to give practically the same result as that obtained by the theory of Brownian motion of harmonic oscillator. Finally, this method is applied to the fluctuation of electronic distribution in metals (the Johnson noice). The correlation function of electric current thus obtained is in accord with that given by Bakker-Heller and by Spenke. The correlation of heat flow and the cross correlation of electric current and heat flow are also given.

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