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- W2014289317 abstract "All solutions describing the electric field of a collisionless Maxwellian or not-Maxwellian onedimensional plasma at stationary equilibrium in a box can be obtained from the requirement that the electrostatic energy has an extremum value under the constraint that I = − ∑i∫δξiGi(n) dx be given, where the Gi(n) are any functions of the density n(x), each Gi(n(x)) being defined for x in the interval Δxi delimited by the zeros of dn/dx or by the walls of the box. The functions Gi may be chosen in an arbitrary way, which is in agreement with the occurrence of an arbitrary function in the most general solution of the relevant mathematical equations. The quantity I describes the “information” which is necessary for a complete description of the electric properties of the physical system. Moreover, it satisfies the following remarkable properties: a) it takes an extremum value at equilibrium with respect to arbitrary variations of the electric field, which, however, should be fixed at the boundaries of each Δxi, under the constraint that the electrostatic energy has a given value; b) in the limit in which thr Penrose stability criterion holds everywhere in the box (linear theory) or can be considered to hold as a local criterion (not too inhomogeneous plasmas) this extremum value is a maximum when the plasma is stable, while if I is minimum the plasma is unstable; c) the extremum value of I with respect to arbitrary variations of n(x), under the constraint that the total number of particles is fixed, corresponds to a completely homogeneous plasma and is connected to the stability problem in the same way as in b). On the ground of these results and according to information theory the quantity I can be assumed as a definition of an entropy which describes the irreversible behaviour of the collisionless plasma, also when situations very far from the statistical equilibrium are considered. Moreover, using this definition of the entropy a quantity F can be introduced the extremum values of which for a fixed volume of the box and fixed kinetic energy of the plasma characterize the equilibrium configurations and which plays formally the same role as the Helmholtz free energy in thermodynamics." @default.
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- W2014289317 date "1965-04-01" @default.
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- W2014289317 title "Information theory and variational properties of a strongly inhomogeneous collisionless plasma" @default.
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- W2014289317 doi "https://doi.org/10.1016/0031-8914(65)90080-7" @default.
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