Hostname: page-component-77c89778f8-gq7q9 Total loading time: 0 Render date: 2024-07-16T15:13:02.274Z Has data issue: false hasContentIssue false
  • English
  • Français

Lagrangian description and entropy of magnetic Vlasov systems

Published online by Cambridge University Press:  13 March 2009

E. Minardi
E. Minardi
Affiliation:
Istituto di Fisica del Plasma, Associazione EUR-ENEA-CNR Via Bassini 15, 20133 Milano, Italy
Get access Rights & Permissions [Opens in a new window]

Abstract

In this paper we study the relation between the collective magnetic entropy of the Vlasov systems, introduced previously on a phenomenological basis, and the Lagrangian description of the motion of a system of independent particles in a magnetic field, subject to a constraint that introduces collective behaviour. The main result is the equivalence of the first variations of the action integral and of the collective entropy with respect to a certain family of variations of the Lagrangian co-ordinates corresponding to reversible variations of the collective system considered as isolated. In the case of irreversible transformations the collective entropy is not determined dynamically, but acquires its meaning through the procedure of maximum probability assignment according to the standard formalism of information theory, under the requirement of macroscopic reproducibility.

Type
Research Article
Information
Journal of Plasma Physics , Volume 48 , Issue 2 , October 1992 , pp. 309 - 323
Copyright
Copyright © Cambridge University Press 1992

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Buck, B. & Macauley, V. A. (eds) 1991 Maximum Entropy in Action. Clarendon.CrossRefGoogle Scholar
Garrett, A. J. M. 1991 Maximum Entropy in Action (ed. Buck, B. & Macaulay, V. A.), p. 139. Clarendon.CrossRefGoogle Scholar
Goldstein, H. 1990 Classical Mechanics, p. 24. Addison-Wesley.Google Scholar
Gull, S. F. 1991 Maximum Entropy in Action (ed. Buck, B. & Macaulay, V. A.), p. 171. Clarendon.CrossRefGoogle Scholar
Jaynes, E. T. 1983 Papers on Probability, Statistics and Statistical Physics (Syntheses Library, vol. 158) (ed. Rosenkrantz, R. D.). Reidel.Google Scholar
Minardi, E. 1989 Plasma Phys. Contr. Fusion 31, 229.CrossRefGoogle Scholar
Minardi, E. 1992 a J. Plasma Phys. 48, 281.CrossRefGoogle Scholar
Minardi, E. 1992 b Plasma Phys. Contr. Fusion 34, 301; 34, 989.CrossRefGoogle Scholar
Minardi, E. & Lampis, G. 1990 Plasma Phys. Contr. Fusion, 32, 918CrossRefGoogle Scholar
Shannon, C. E. 1948 Bell Syst. Tech. J. 27, 379 and 623 (Reprinted in C. E. Shannon & W. Weaver. The Mathematical Theory of Communication. University of Illinois Press, 1949).Google Scholar