SINCE ANCIENT TIMES describing the behavior of macroscopic matter in terms of dynamic principles that govern its microscopic constituents has fascinated physicists. Foundations of the modern understanding were laid by Ludwig Boltzmann in the latter part of the 19th century. From physical arguments concerning the probable number of binary collisions (the Stosszahlansatz based on the principle of molecular chaos), Boltzmann deduced a “kinetic” equation satisfied by the probability distribution function.
REFERENCES
1.
L. Boltzmann, Lectures on Gas Theory, University of California Press, Berkeley (1964).
2.
M.
Lewis
, Phys. Rev.
134A
, 1410
(1964
).3.
P. Ehrenfest, T. Ehrenfest, The Conceptual Foundations of the Statistical Approach hi Mechanics, Cornell University Press, Ithaca, N.Y. (1959).
4.
N. Bogolyubov, Problems of a Dynamical Theory in Statistical Physics, Moscow (1946), English translation by E. Gora in Studies in Statistical Mechanics, vol. 1 (J. deBoer, G. Uhlenbeck, eds.) North‐Holland Publishing Co., Amsterdam (1962).
5.
6.
J. Jeans, Kinetic Theory of Gases, Cambridge University Press, London (1946);
S. Chapman, T. Cowling, The Mathematical Theory of Nonuniform Gases, Cambridge University Press, London (1958);
J. Hirschfelder, C. Curtiss, R. Bird, Molecular Theory of Gases and Liquids, John Wiley and Sons, New York (1954).
7.
S. Choh, G. Uhlenbeck, The Kinetic Theory of Phenomena in Dense Gases, University of Michigan, Navy Theoretical Physics Contract No. NONR 1224 (15) (1958);
8.
G. Sandri, The New Foundations of Statistical Dynamics, mimeographed Rutgers lectures (1961–62);
9.
10.
11.
J. van Leeuwen, A. Weijland, Phys. Letters (to appear, 1966);
12.
J. McCune, G. Sandri, E. Frieman in Rarefied Gas Dynamics, vol. 1, (J. Laurmann, ed.), Academic Press, New York (1963);
G. Sandri, The Supersecularities in Weak Coupling Kinetic Theory, ARAP (Aeronautical Research Associates of Princeton) report 46, (1963);
S.
Fujita
, Phys. Letters
2
, 300
(1964
);C.
Su
, Phys. Fluids
7
, 1227
(1964
);K.
Kawasaki
, I.
Oppenheim
, Phys. Rev.
139A
, 1763
(1965
);G. Sandri, “The Physical Foundations of Modern Kinetic Theory” in Proceedings of the Symposium on the Dynamics of Fluids and Plasmas (dedicated to J. Burgers), (University of Maryland, 1965) (S. Pai, ed.) Academic Press, New York (1966);
13.
14.
A. Lenard, private communication;
15.
G. Sandri, R. Sullivan, A. Kritz, F. Schatzman, Statistical Mechanical Theory of Dense Plasmas, ARAP report 74 (1965).
16.
L. Van Hove, N. Hugenholtz, L. Howland, Quantum Theory of Manyparticle Systems, W. Benjamin, New York (1961);
17.
I. Prigogine, Nonequilibrium Statistical Mechanics, Interscience, New York (1962);
18.
P. Goldberg, G. Sandri, to be published.
19.
C. Wu, E. Klevans in Proceedings of the 6th International Conference on Ionization Phenomena in Gases, SERMA, Paris (1964).
20.
J. McCune, T. Morse, G. Sandri, in Rarefied Gas Dynamics, vol. 1, op cit ref. 12;
D. Book, MATT report 274, Princeton University (1964);
D.
Frank
, D.
Pfirsch
, S.
Priess
, Naturforsch.
20a
, 147
(1965
);D.
Montgomery
, D.
Tidman
, Phys. Fluids
2
, 242
(1964
);D. Montgomery, Connection between the Bogolyubov and the Frieman and Sandri Methods, preprint (1965);
P. Schram, Euratom report Eur. 19O5.e (1964).
21.
22.
G. Sandri, A New Fundamental Principle in Kinetic Theory, ARAP report 37 (1962);
Bull. Am. Phys. Soc.
8
, 151
(1963
);23.
F. Engelman, G. Sandri, unpublished.
24.
E. Frieman, R. Goldman, private communication to be published;
G. V. Ramanathan, G. Sandri, to be published;
25.
J.
Hubbard
, Proc. Roy. Soc. (London)
A261
, 371
(1961
);26.
E.
Boldt
, G.
Sandri
, Phys. Rev.
135B
, 1086
(1964
).27.
G. Sandri, Uniformization of Asymptotic Expansions, paper presented at 2d Symposium on Nonlinear Partial Differential Equations (University of Delaware, 1965) (proceedings published by Academic Press, New York, 1965, W. Ames, ed.);
M. Van Dyke, Perturbation Methods in Fluid Dynamics, Academic Press, New York (1964).
28.
W.
Thurston
, G.
Sandri
, Classical Hard‐sphere Three‐body Problem, Bull. Am. Phys. Soc.
9
, 386
(1964
);G.
Sandri
, R.
Sullivan
, Notices Am. Math. Soc.
12
, 215
(1965
);D. Foch, private communication;
G. Sandri, A. Kritz, An Approach to the N‐body Problem with Hard Sphere Interaction, ARAP report 86 (1966) (to be published in Phys. Rev.);
T. Murphy, to be published.
29.
P.
Woodrow
, R.
Sullivan
, G.
Sandri
, SIAM Review
7
, 620
(1965
).30.
G. Sandri, On the Relationship between the Single Relaxation Time Equation and Liouville's Theorem, ARAP report 80 (1966).
31.
H. Grad in Handbuch der Physik, vol. 12, Springer‐Verlag, Berlin (1957);
32.
W. Pauli, Probleme der Modernen Physik, S. Hirzel, Leipzig (1928);
I.
Oppenheim
, K.
Shuler
, Phys. Rev.
138B
, 1008
(1965
);33.
R. Ong, paper T4 at annual meeting of Plasma Physics Division, American Physical Society, November 1964.
34.
G. Uhlenbeck, Lectures on the Statistical Mechanics of Nonequilibrium Phenomena (unpublished lecture notes), University of Michigan.
35.
G. Sandri, Kinetic Models for Gaseous Mixtures, ARAP note 62‐4 (1962);
G. Sandri, A. Kritz, F. Schatzman, Kinetic Thermodynamics, ARAP report 78 (1965) (to be published).
36.
J. Luttinger, private communication.
This content is only available via PDF.
© 1966 American Institute of Physics.
1966
American Institute of Physics
You do not currently have access to this content.
