Boltzmann H function and entropy in the plasma sheet

Boltzmann's H function was evaluated using 10 years of 1-min distribution functions. These results were used to study the long-term averaged spatial distributions of four entropy parameters. The average entropy density s(a)(x), where a = i for ions and a = e for electrons, increased when moving Earthward or toward the flanks. The magnitudes of these entropy changes were similar for ions and electrons. The entropy per unit flux tube S-f,S-a(x) decreased when moving Earthward or toward midnight. The spatial changes of s(a)(x) and of S-f,S-a(x) were attributed primarily to variations of the particle density n(a)(x) and of the particle content of each unit flux tube N-f(x), respectively. A dimensionless parameter (S/Nc(v))(H,i) that is proportional to the average entropy per ion increased when moving Earthward or toward midnight near the neutral sheet. The dimensionless parameter proportional to the entropy per ion that would exist in a plasma with the measured pressure and density but with a Maxwellian distribution function (S/Ncv)(P,i) was also calculated. Differences between (S/Ncv)(P,i) and (S/Nc(v))(H,i) showed that the plasma was closer to equilibrium near the neutral sheet at x = -10 RE than at x = -28 R-E. These gradients of the entropy per ion and of the deviations from equilibrium suggest that nonadiabatic processes and particle scattering are significant throughout the region studied.