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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
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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

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