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Teoreticheskaya i Matematicheskaya Fizika, 1995, Volume 103, Number 1, Pages 109–122
(Mi tmf1290)
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Theory of nonequilibrium phenomena based on the BBGKI hierarchy. I. Small deviation from equilibrium
G. A. Martynov Institute of Physical Chemistry, Russian Academy of Sciences
Abstract:
The BBGKY hierarchy is expanded in a series with respect to the small parameter ε=σ/L, where σ is the diameter of the particles, and L is a characteristic macroscopic length (for example, the diameter of the system). Since neither σ, nor L occurs explicitly in the equations of the hierarchy, a preliminary step consists of separation from the distribution functions G(l) of short-range components that vary over distances of order σ and long-range components that vary over distances of order L. By a transition to dimensionless variables, terms of zeroth and first order in ε in the hierarchy are separated, this making it possible to perform the expansion with respect to ε. It is shown that in the zeroth order in ε the BBGKY hierarchy determines a state of local equilibrium that for any matter density can be described by a Maxwell distribution “with shift”. The higher terms of the series in ε describe the deviations from local equilibrium. At the same time, the long-range correlations that always arise in nonequilibrium systems are described by the balance equations for mass, momentum, and energy, which are also a consequence of the BBGKY hierarchy, whereas the short-range correlations are described by the equations for G(l) obtained from the same hierarchy by expanding G(l) in a series with respect to ε.
Received: 19.04.1994
Citation:
G. A. Martynov, “Theory of nonequilibrium phenomena based on the BBGKI hierarchy. I. Small deviation from equilibrium”, TMF, 103:1 (1995), 109–122; Theoret. and Math. Phys., 103:1 (1995), 433–443
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https://www.mathnet.ru/eng/tmf1290 https://www.mathnet.ru/eng/tmf/v103/i1/p109
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Abstract page: | 318 | Full-text PDF : | 123 | References: | 47 | First page: | 1 |
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