ISSN:
1573-9333
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
,
Physics
Notes:
Abstract The BBGKY hierarchy is expanded in a series with respect to the small parameter $$\varepsilon = {\sigma \mathord{\left/ {\vphantom {\sigma \mathcal{L}}} \right. \kern-\nulldelimiterspace} \mathcal{L}}$$ , where σ is the diameter of the particles, and $$\mathcal{L}$$ is a characteristic macroscopic length (for example, the diameter of the system). Since neither σ 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 σ 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 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 $$\mathcal{G}_{(l)} $$ obtained from the same hierarchy by expanding $$\mathcal{G}_{(l)} $$ in a series with respect to ε.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF02069787
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