Abstract
Up to date (1987), I list references on the rigorous microscopic derivation of the Boltzmann equation from the mechanical model of hard sferes with elastic collisions, resp. of classical particles interacting through a smooth pair potential.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
O.E. Lanford, Time evolution of large classical systems, In: Dynamical Systems and Applications, ed. J. Moser, Lecture Notes in Physics Vol. 38, 1–111. Springer, Berlin, 1975.
O.E. Lanford, On a derivation of the Boltzmann equation, Astérisque, 40, 117–137 (1976)
Nonequilibrium Phenomena I, The Boltzmann Equation, eds. J.L. Lebowitz and E.W. Montroll, Studies in Statistical Mechanics X, North-Holland, Amsterdam, 1983.
O.E. Lanford, Notes of the lectures at the troisième cycle at Lausanne, 1978, unpublished.
O.E. Lanford, Hard-sphere gas in the Boltzmann-Grad limit, Physica 106A, 70–76 (1981).
F. King, BBGKY hierarchy for positive potentials, PH. D. thesis, Dept. of Mathematics, Univ. of California at Berkeley, 1975.
R. Illner and M. Pulvirenti, A derivation of the BBGKY-hierarchy for hard sphere particle systems, preprint Univ. of Victoria, 1985, to appear in Transport Theory and Statistical Physics:
H.Spohn, On the integrated form of the BBGKY hierarchy for hard spheres, preprint.
K. Uchiyama, On the derivation of the Boltzmann equation from a deterministic motion of many particles, Taniguchi Symp. PMMP Katata 1985, p. 421–441.
K. Uchiyama, Derivation of the Boltzmann equation from particle dynamics, preprint, 1987. The technical machinery developed in [1] and [6] has been used to tackle related problems. (i) fluctuation theory for the Boltzmann equation.
H. van Beijeren, O.E. Lanford, J.L. Lebowitz, H. Spohn, Equilibrium time correlation functions in the low density limit, J. Stat. Phys. 22, 237–257 (1980).
H. Spohn, Fluctuations around the Boltzmann equation, J. Stat. Phys. 26, 285–305 (1981).
H. Spohn, Fluctuation theory for the Boltzmann equation, in [3].
H. Spohn, Boltzmann equation and Boltzmann hierarchy. In “Kinetic Theories and the Boltzmann Equation”, eds. C. Cercignani, Lecture Notes in Math. 1048, p. 207–220, Springer, Berlin, 1984.
G. Gallavotti, Rigorous theory of the Boltzmann equation in the Lorentz gas, Nota interna n. 358, Univ. di Roma and Phys. Rev. 185, 308 (1969).
H. Spohn, The Lorentz process converges to a random flight process, Comm. Math. Phys. 60, 277–290 (1978).
H. Babovsky, Diplomarbeit, Univ. Kaiserslautern, 1980.
J.L. Lebowitz and H. Spohn, Steady state self-diffusion at low density, J. Stat. Phys. 29, 39–55, (1982).
C. Boldrighini, L.A. Bunimovich, Y.G. Sinai, On the Boltzmann equation for the Lorentz gas, J. Stat. Phys. 32, 477 (1983).
R. Illner and M. Pulvirenti, Global validity of the Boltzmann equation for a two-dimensional rare gas in vacuum, Comm. Math. Phys. 105, 189–203 (1986).
M. Pulvirenti, Global validity of the Boltzmann equation for a three-dimensional rare gas in vacuum, Comm. Math. Phys. 113, 79–85 (1987).
J.L. Lebowitz and H. Spohn, On the time evolution of macroscopic systems, Comm. Pure Appl. Math. 36, 593–613 (1983).
C. Cercignani, The Grad limit for a system of soft spheres, Comm. Pure Appl. Math. 36, 479–494 (1983).
K. Uchiyama, On the Boltzmann-Grad limit for the Broadwell of the Boltzmann equation, preprint, 1987.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1988 Springer-Verlag Wien
About this chapter
Cite this chapter
Spohn, H. (1988). Microscopic Derivation of the Boltzmann Equation. In: Cercignani, C. (eds) Kinetic Theory and Gas Dynamics. International Centre for Mechanical Sciences, vol 293. Springer, Vienna. https://doi.org/10.1007/978-3-7091-2762-9_7
Download citation
DOI: https://doi.org/10.1007/978-3-7091-2762-9_7
Publisher Name: Springer, Vienna
Print ISBN: 978-3-211-82090-2
Online ISBN: 978-3-7091-2762-9
eBook Packages: Springer Book Archive