Hostname: page-component-848d4c4894-hfldf Total loading time: 0 Render date: 2024-05-11T10:43:45.462Z Has data issue: false hasContentIssue false
  • English
  • Français

Absolute equilibrium entropy

Published online by Cambridge University Press:  13 March 2009

John V. Shebalin
John V. Shebalin
Affiliation:
National Aeronautics and Space Administration, Langely Reserach Center, Hampton, Virginia 23681, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

The entropy associated with absolute equilibrium ensemble theories of ideal, homogeneous, fluid and magnetofluid turbulence is discussed, and the three-dimensional fluid case is examined in detail. A σ function is defined, whose minimum value with respect to global parameters is the entropy. A comparison is made between the use of global functions σ and phase functions H (associated with the development of various H theorems of ideal turbulence). It is shown that the two approaches are complementary, though conceptually different: H theorems show that an isolated system tends to equilibrium, while σ functions allow the demonstration that entropy never decreases when two previously isolated systems are combined. This provides a more complete picture of entropy in the statistical mechanics of ideal fluids.

Type
Research Article
Information
Journal of Plasma Physics , Volume 56 , Issue 3: Special Issue: Honour of David Montgomery , December 1996 , pp. 419 - 426
Copyright
Copyright © Cambridge University Press 1996

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Betchov, R. 1961 Phys. Fluids 4, 925.CrossRefGoogle Scholar
Carnevale, G. F. 1982 J. Fluid Mech. 122, 143.Google Scholar
Carnevale, G. F., Frisch, U. and Salmon, R. 1981 J. Phys. A: Math. Gen. 14, 1701.CrossRefGoogle Scholar
Elsässer, W. M. 1956 Rev. Mod. Phys. 28, 135.CrossRefGoogle Scholar
Frisch, U., Pouquet, A., Leorat, J. and Mazure, A. 1975 J. Fluid Mech. 68, 769.CrossRefGoogle Scholar
Fyfe, D. and Montgomery, D. 1976 J. Plasma Phys. 16, 181.CrossRefGoogle Scholar
Khinchin, A. I. 1949 Mathematical Foundations of Statistical Mechanics, pp. 137–145. Dover, New York.Google Scholar
Kraichnan, R. H. 1973 J. Fluid Mech. 59, 745.CrossRefGoogle Scholar
Kraichnan, R. H. 1975 J. Fluid Mech. 67, 155.CrossRefGoogle Scholar
Kraichnan, R. H. and Montgomery, D. 1980 Rep. Prog. Phys. 43, 547.CrossRefGoogle Scholar
Landau, L. D. and Lifshitz, E. M. 1980 Statistical Physics, p. 27. Pergamon, Oxford.Google Scholar
Landau, L. D. and Lifshitz, E. M. 1987 Fluid Mechanics, pp. 3–4, Pergamon, Oxford.Google Scholar
Lee, T. D. 1952 Q. Appl. Maths 10, 69.CrossRefGoogle Scholar
Lifshitz, E. M. and Pitaevskii, L. P. 1981 Physical Kinetics, p. 11. Pergamon, Oxford.Google Scholar
Moffatt, H. K. 1969 J. Fluid Mech. 35, 117.CrossRefGoogle Scholar
Montgomery, D. 1976 Phys. Fluids 19, 802.Google Scholar
Shebalin, J. V. 1989 Physica D37, 173.Google Scholar
Shebalin, J. V. 1994 Phys. Plasmas 1, 541.Google Scholar
Shebalin, J. V., Matthaeus, W. H. and Montgomery, D. 1983 J. Plasma Phys. 29, 525.Google Scholar
Sinai, Ya. G. 1994 Topics in Ergodic Theory. Princeton University Press.CrossRefGoogle Scholar
Woltjer, L. 1958 Proc. Natl Acad. Sci. USA 44, 833.Google Scholar