Thermodynamic equilibrium under long-range forces. III. Equivalence of self-consistent-field and fixed-external-field formulations

Physics – Optics

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Other Topics In Statistical Physics, Thermodynamics, And Nonlinear Dynamical Systems, Other Topics In General Relativity And Gravitation, Other Topics In Electromagnetism, Electron And Ion Optics

Scientific paper

The equilibrium state of a system is determined by requiring the entropy to be maximum under an infinitesimal variation. Properly speaking, the variation of the thermodynamic variables of a system under a long-range force should be accompanied by a variation of the long-range force fields so as to maintain the field equations (self-consistent-field variation). These problems are, however, often treated by restricting the variations to a small region and ignoring the corresponding field variations (fixed-external-field variation). The equivalence between the two formulations is found to be nontrivial and sometimes only of a limited nature.

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