Particle acceleration and entropy considerations

Possible entropy constraints on particle acceleration spectra are discussed. Solar flare models invoke a variety of initial distributions of the primary energy release over the particles of the flare plasma -- ie., the partition of the energy between thermal and nonthermal components. It is suggested that, while this partition can take any value as far as energy is concerned, the entropy of a particle distribution may provide a useful measure of the likelihood of its being produced for a prescribed total energy. The Gibbs' entropy is calculated for several nonthermal isotropic distribution functions $f$, for a single particle species, and compared with that of a Maxwellian, all distributions having the same total number and energy of particles. Speculations are made on the relevance of some of the results to the cosmic ray power-law spectrum, on their relation to the observed frequency distribution of nonthermal flare hard X-ray spectrum parameters and on the additional energy release required to achieve lower entropy $f$s.