Entropies for Continua: Fluids and Magnetofluids
Bartol Research Institute
University of Delaware
The greatest single use of maximum entropy methods at present seems to
be in situations related to data analysis. However, for over twenty
years it has also appeared  that considerations of maximum entropy
might have dynamical implications for dissipative continuum mechanics
that go beyond the class of statements that can be made from the
traditional statistical mechanics of discrete particles. Inquiry into
the extent to which a meaningfully increasing entropy can be defined
for an evolving dissipative continuum has been to a considerable
degree an ``experimental'' investigation [2,3], with numerical
solution of the relevant dynamical equations (e.g., Navier-Stokes,
magnetohydrodynamic, geostrophic or plasma ``drift'' equations) as
the principal experimental tool. Here, we review various suggested
formulations and the accumulated numerical evidence. We also suggest
theoretical and computational problems currently thought to be
potentially illuminating and ripe for solution.
 G. Joyce and D. Montgomery, J. Plasma Phys. 10, 107 (1973); D.
Montgomery, in Maximum-Entropy and Bayesian Methods in Inverse
Problems, ed. by C. Ray Smith and W.T. Grandy, Jr. (Dordrecht; D.
Reidel, 1985), pp. 455-468.
 W.H. Matthaeus et al, Phys. Rev. Lett. 66, 2731 (1991) and Physica
D 51, 531 (1991)
 D. Montgomery et al, Phys. Fluids A 4, 3 (1992); D. Montgomery, X.
Shan and W.H. Matthaeus, Phys. Fluids A 5, 2207 (1993)
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