Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy methods for sums of Lyapunov exponents for dilute gases

Chaos
J R DorfmanH van Beijeren

Abstract

We consider a general method for computing the sum of positive Lyapunov exponents for moderately dense gases. This method is based upon hierarchy techniques used previously to derive the generalized Boltzmann equation for the time-dependent spatial and velocity distribution functions for such systems. We extend the variables in the generalized Boltzmann equation to include a new set of quantities that describe the separation of trajectories in phase space needed for a calculation of the Lyapunov exponents. The method described here is especially suitable for calculating the sum of all of the positive Lyapunov exponents for the system, and may be applied to equilibrium as well as nonequilibrium situations. For low densities we obtain an extended Boltzmann equation, from which, under a simplifying approximation, we recover the sum of positive Lyapunov exponents for hard-disk and hard-sphere systems, obtained before by a simpler method. In addition we indicate how to improve these results by avoiding the simplifying approximation. The restriction to hard-sphere systems in d dimensions is made to keep the somewhat complicated formalism as clear as possible, but the method can be easily generalized to apply to gases of particles tha...Continue Reading

References

Apr 1, 1989·Physical Review A: General Physics·D ThirumalaiT R Kirkpatrick
Nov 15, 1990·Physical Review. a·D J EvansG P Morriss
Jan 1, 1995·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·J R Dorfman, P Gaspard
Oct 1, 1995·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·P Gaspard, J R Dorfman
Feb 1, 1996·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·C DellagoW G Hoover
May 29, 1995·Physical Review Letters· van Beijeren H, J R Dorfman
Sep 2, 1996·Physical Review Letters· van Beijeren HC Dellago

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Citations

Apr 17, 2001·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·H van BeijerenJ R Dorfman
Oct 4, 2005·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Astrid S de Wijn
Aug 27, 2011·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Arul Lakshminarayan, Steven Tomsovic
Sep 26, 2012·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·G P Morriss
Aug 7, 2007·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·A FingerleV Yu Zaburdaev
Dec 31, 2005·Physical Review Letters·Axel FingerleVasily Zaburdaev
May 21, 2005·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Astrid S de Wijn
Dec 20, 2003·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Pierre Gaspard

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