Time Evolution in Macroscopic Systems. III: Selected Applications
- W. T. Grandy Jr.
- … show all 1 hide
Rent the article at a discountRent now
* Final gross prices may vary according to local VAT.Get Access
The results of two recent articles expanding the Gibbs variational principle to encompass all of statistical mechanics, in which the role of external sources is made explicit, are utilized to further explicate the theory. Representative applications to nonequilibrium thermodynamics and hydrodynamics are presented, describing several fundamental processes, including hydrodynamic fluctuations. A coherent description of macroscopic relaxation dynamics is provided, along with an exemplary demonstration of the approach to equilibrium in a simple fluid.
- J. W. Gibbs, Elementary Principles in Statistical Mechanics (Yale University Press, New Haven, CT, 1902).
- C. Shannon, “Mathematical theory of communication,” Bell System Tech. J. 27, 3, 79, 623 (1948).
- E. T. Jaynes, “Information theory and statistical mechanics,” Phys. Rev. 106, 620(1957).
- J. E. Shore and R. W. Johnson, “Axiomatic derivation of the principle of maximum entropy and the principle of minimum cross-entropy,” IEEE Trans. Inf. Th. IT-26, 26(1980).
- W. T. Grandy, Jr., “Time evolution in macroscopic systems. I: Equations of motion,” Found. Phys. 34, 1(2004).
- W. T. Grandy, Jr., “Time evolution in macroscopic systems. II: The entropy,” Found. Phys. 34, 21(2004).
- J. W. Gibbs, “On the equilibrium of heterogeneous substances,” Trans. Conn. Acad. Sci. III, 108, 343 (1875-1878) [reprinted in The Scientific Papers of J. Willard Gibbs, Vol. vn1 (Dover, NY, 1961)].
- E. T. Jaynes, “Information theory and statistical mechanics. II,” Phys. Rev. 108, 171(1957).
- F. Schlögl, “Produced entropy in quantum statistics,” Z. Phys. 249, 1(1971).
- E. Pfaffelhuber, “Information-theoretic stability and evolution criteria in irreversible thermodynamics,” J. Stat Phys. 16, 69(1977).
- W. C. Mitchell, “Statistical mechanics of thermally driven systems,” Ph.D. thesis (Washington University, St. Louis, MO, 1967).
- S. P. Heims and E. T. Jaynes, “Theory of gyromagnetic effects and some related magnetic phenomena,” Rev. Mod. Phys. 34, 143(1962).
- W. T. Grandy, Jr., Foundations of Statistical Mechanics, Vol. II: Nonequilibrium Phenomena (Reidel, Dordrecht, 1988).
- C. Truesdell, Rational Thermodynamics (Springer, New York, 1984).
- D. Jou, J. Casas-Vásquez, and G. Lebon, Extended Irreversible Thermodynamics (Springer, Berlin, 2001).
- R. D. Puff and N. S. Gillis, “Fluctuations and transport properties of many-particle systems,” Ann. Phys. (N.Y.) 6, 364(1968).
- W. T. Grandy, Jr., Foundations of Statistical Mechanics, Vol. I: Equilibrium Theory (Reidel, Dordrecht, 1987).
- L. D. Landau and E. M. Lifshitz, “Hydrodynamic fluctuations,” Sov. Phys. JETP 5, 512(1957) [Zh. Eksp. Teor. Fiz. 32, 618(1957)]. See, also, Fluid Mechanics (Pergamon, New York, 1959).
- G. Quentin and I. Rehberg, “Direct measurement of hydrodynamic fluctuations in a binary mixture,” Phys. Rev. Lett. 74, 1578(1995).
- V. G. Morozov, “On the Langevin formalism for nonlinear and nonequilibrium hydrodynamic fluctuations,” Physica A 126, 443(1984).
- R. F. Fox, “Hydrodynamic fluctuation theories,” J. Math. Phys. 19, 1993(1978).
- R. Schmitz and E. G. D. Cohen, “Fluctuations in a fluid under a stationary heat flux. I. General theory,” J. Stat. Phys. 38, 285(1985).
- J. A. Snow, “Sound absorption in model quantum systems,” Ph.D. thesis (Washington University, St. Louis, MO, 1967).
- E. T. Jaynes, “Where do we stand on maximum entropy?,” in The Maximum Entropy Formalism, R. D. Levine and M. Tribus, eds. (M.I.T. Press, Cambridge, MA, 1979).
- Time Evolution in Macroscopic Systems. III: Selected Applications
Foundations of Physics
Volume 34, Issue 5 , pp 771-813
- Cover Date
- Print ISSN
- Online ISSN
- Kluwer Academic Publishers-Plenum Publishers
- Additional Links
- nonequilibrium statistical mechanics
- hydrodynamic fluctuations
- approach to equilibrium
- Industry Sectors
- W. T. Grandy Jr. (1)
- Author Affiliations
- 1. Department of Physics & Astronomy, University of Wyoming, Laramie, Wyoming, 82071