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By Max Born, H. S. Green

This paper outlines a normal conception whose item is to supply a foundation from which the entire equilibrium and dynamical houses of drinks could be investigated. a suite of multiform distribution capabilities is outlined, and the generalized continuity equations chuffed by means of those capabilities are derived. through introducing the equations of movement, a collection of kinfolk is received from which the distribution features could be made up our minds. it's proven that Boltzmann's equation within the kinetic thought of gases follows as a specific case, and that, in equilibrium stipulations, the idea provides effects in keeping with statistical mechanics. An crucial equation for the radial distribution functionality is got that is the ordinary generalization of 1 acquired by means of Kirkwood for 'rigid round molecules'. eventually, it really is indicated how the idea could be utilized to unravel either equilibrium and dynamical difficulties of the liquid kingdom.

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Sci. 1 Introduction In Chap. 6), valid for single variable linear systems. We shall extend the approach used there to multi-variable systems in Chap. 4 and use the results later for comparison with experiments on relative stability. However, the generalization of the results in Chap. 2 for multi-variable linear and non-linear systems, based on the use of deterministic kinetic equations, does not yield a thermodynamic state function. In order to obtain a thermodynamic state function for multi-variable systems we need to consider fluctuations, and now turn to this analysis [1].

2) and obtain W (X − r, r) PX (X − r, t) = dxW (xV, r) Px (x, t) ∞ + dx m (−1) m! m=1 1 r · ∇x V m [W (xV, r) Px (x, t)] . 6) with which we can write ∞ 1+ (−1) m! m=1 m 1 r · ∇x V ∞ m . . . = 1+ 1 m (r · p ˆ ) . . . = exp (r · p ˆ) . . m! 8) where we have defined the Hamiltonian operator (2–4) w (x, r; V ) [exp (r · p ˆ ) . . − 1] . ˆ + (x, p H ˆ) . . 9) r Thus we have formally, and exactly, converted the master equation to a Schroedinger equation. This has the substantial advantage that we can apply well-known approximations in quantum mechanics to obtain solutions to the master equation.

L. Stein, Phys. Rev. Lett. 69, 3691–3695 (1992) 11. R. Jauslin, Physica A. 144, 179–191 (1987) 12. R. Jauslin, J. Stat. Phys. 42, 573–585 (1986) 13. I. D. Wentzell, Random Perturbations of Dynamical Systems (Springer, Berlin Heidelberg New York, 1984) 14. G. C. L. Lions, Trans. AMS. 282, 487–502 (1984) 4 Continuation of Deterministic Approach for Multivariable Systems In Chap. 2 we analyzed single variable linear and non-linear systems with single and multiple stable stationary states by use of the deterministic equations of chemical kinetics.

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