Entropies for Continua: Fluids and Magnetofluids

D. Montgomery
Dartmouth College
Hanover
NH 03755
USA

X. Shan
Dartmouth College
Hanover
NH 03755
USA

W.H. Matthaeus
Bartol Research Institute
University of Delaware
Newark
DE 19716
USA

Abstract

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 [1] 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.

References

[1] 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.

[2] W.H. Matthaeus et al, Phys. Rev. Lett. 66, 2731 (1991) and Physica D 51, 531 (1991)

[3] D. Montgomery et al, Phys. Fluids A 4, 3 (1992); D. Montgomery, X. Shan and W.H. Matthaeus, Phys. Fluids A 5, 2207 (1993)


MaxEnt 94 Abstracts / mas@mrao.cam.ac.uk