Kinetic Equations from Hamiltonian Dynamics: The Markovian Approximations
The goal of non-equilibrium statistical mechanics is to explain the macroscopic behavior of matter from the dynamics of its microscopic constituents, i.e. atoms or molecules. Because of the large number of particles involved, this is a rather ambitious program. Therefore, as an intermediate step, one tries to write down an approximately valid dynamics as governed by a kinetic equation. Examples are the Boltzmann equation for a dilute gas, the hydrodynamic equations for an “aged” fluid, etc., There is a lot known about the interrelationship between the microscopic and kinetic description of a physical system and it would be rather hopeless to press all these results into one lecture. Therefore I would like to do three things.
KeywordsKinetic Equation Boltzmann Equation Hard Sphere Specular Reflection Weak Coupling Limit
Unable to display preview. Download preview PDF.
- F. King, BBGKY hierarchy for positive potentials. Ph. D. Thesis, Dep. of Math., Univ. of Cal. at Berkeley (1975)Google Scholar
- H. van Beijeren, O. E. Lanford, J. L. Lebowitz, H. Spohn, Equilibrium time correlation functions in the low density limit, preprint (1979)Google Scholar
- H. Spohn, Kinetic equations from Hamiltonian dynamics: The Markovian limit. Lecture Notes, University of Leuven, 1979Google Scholar
- G. Papanicalaou, private communicationGoogle Scholar
- H. Neunzert, Neuere qualitative und numerische Methoden in.er Plasmaphysik, Vorlesungsmanuskript Paderborn, 1975Google Scholar
- E. H. Hauge, What can one learn from Lorentz models? In; Transport Phenomena, ed. L. Garrido, Lecture Notes in Physics 31, p. 338. Springer, Berlin (1974)Google Scholar
- R. K. Alexander, The infinite hard sphere system. Ph. D. Thesis, Dep. of Math. Univ. of Cal. at Berkeley (1975)Google Scholar
- O. E. Lanford, Notes of the lectures at the troisième cycle at Lausanne, 1978, unpublishedGoogle Scholar
- N. G. van Kampen, Phys. Lett. A13, 458 (1976)Google Scholar
- M. Kac, J. Logan, Fluctuations. Studies in Statistical Mechanics, to appearGoogle Scholar
- M. Kac, Fluctuations near and far from equilibrium. In: Statistical Mechanics and Statistical Methods in Theory and Application. Ed. U. Landman. Plenum Press, New York (1977)Google Scholar