Theory of nonequilibrium phenomena based on the BBGKY hierarchy. I. Small deviations from equilibrium

Journal Article · Sun Oct 01 04:00:00 EDT 1995 · Theoretical and Mathematical Physics

DOI:https://doi.org/10.1007/BF02069787· OSTI ID:379183

Martynov, G A

The BBGKY hierarchy is expanded in a series with respect to the smallparameter {xi}={sigma}/{Lambda}, where {sigma} is the diameter of the particles, and {Lambda} is a characteristic macroscopic length (for example, the diameter of the system). Since neither {sigma} nor {Lambda} occurs explicitly in the equations of the hierarchy, a preliminary step consists of separation from the distribution functions G{sub l} of short-range components that vary over distances of order {sigma} and long-range components that vary over distances of order {Lambda}. By a transition to dimensionless variables, terms of zeroth and first order in {var_epsilon} in the hierarchy are separated, this making it possible to perform the expansions with respect to {var_epsilon}. It is shown that in the zeroth order in {var_epsilon} the BBGKY hierarchy determines a state of local equilibrium that for any matter density can be described by a Maxwell distribution {open_quotes}with shift.{close_quotes} The higher terms of the series in {var_epsilon} describe the deviations from local equilibrium. At the same time, the long-range correlations that always arise 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{sub l} obtained from the same hierarchy by expanding G{sub l} in a series with respect to {var_epsilon}.

• Sponsoring Organization: USDOE
• OSTI ID: 379183
• Journal Information: Theoretical and Mathematical Physics, Journal Name: Theoretical and Mathematical Physics Journal Issue: 1 Vol. 103; ISSN 0040-5779; ISSN TMPHAH
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
99 GENERAL AND MISCELLANEOUS
BBGKY EQUATION
DISTRIBUTION FUNCTIONS
EQUATIONS OF MOTION
SERIES EXPANSION