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 TMF, 1995, Volume 103, Number 1, Pages 109–122 (Mi tmf1290)

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 $\varepsilon =\sigma / \mathcal L$, where $\sigma$ is the diameter of the particles, and $\mathcal L$ is a characteristic macroscopic length (for example, the diameter of the system). Since neither $\sigma$, nor $\mathcal L$ occurs explicitly in the equations of the hierarchy, a preliminary step consists of separation from the distribution functions $\mathcal G_{(l)}$ of short-range components that vary over distances of order $\sigma$ and long-range components that vary over distances of order $\mathcal L$. By a transition to dimensionless variables, terms of zeroth and first order in $\varepsilon$ in the hierarchy are separated, this making it possible to perform the expansion with respect to $\varepsilon$. It is shown that in the zeroth order in $\varepsilon$ 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 $\varepsilon$ 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 $\mathcal G_{(l)}$ obtained from the same hierarchy by expanding $\mathcal G_{(l)}$ in a series with respect to $\varepsilon$.

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English version:
Theoretical and Mathematical Physics, 1995, 103:1, 433–443

Bibliographic databases:

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

Citation in format AMSBIB
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