Modeling in Nonequilibrium Thermodynamics

  • François E. Cellier


Until now, we have dealt with applications from either classical mechanics or electrical circuits exclusively. In this chapter, we shall discuss nonequilibrium state thermodynamics. Most engineering students consider thermodynamics a rather difficult topic. The reason for this seeming difficulty lies in the fact that basically all available treatises of thermodynamics have been written by physicists rather than by engineers. Physicists are, by education, phenomenologically rather than systemically oriented. They do not wish to change the world, only to understand it. Therefore, their approach to dealing with problems is quite different from ours. Rather than looking at a system as a whole and trying to analyze the couplings of its subsystems (as we engineers do), they always try to single out individual phenomena and discuss those in isolation. As a consequence, most physics texts present the topic through a collection of various formulae, which are all individually correct and meaningful but hard to relate to each other. It is the aim of this chapter to bridge the gap between those individually well—known equations that govern the behavior of nonequilibrium state thermodynamic systems. According to Jean Thoma, another reason why most thermodynamics textbooks are obscure is the fact that they avoid to work with entropy flow as a physical variable.


Storage Tank Power Flow Time Reversal Nonequilibrium Thermodynamic Bond Graph 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [8.1]
    Peter C. Breedveld (1984), Physical Systems Theory in Terms of Bond Graphs, Ph.D. dissertation, University of Twente, Enschede, The Netherlands.Google Scholar
  2. [8.2]
    François E. Cellier (1990), “Hierarchical Nonlinear Bond Graphs — A Unified Methodology for Modeling Complex Physical Systems,” Proceedings European Simulation MultiConference, Nürnberg, F.R.G., pp. 1–13.Google Scholar
  3. [8.3]
    N. Curie and Hubert J. Davies ( 1968, 1971), Modern Fluid Dynamics, two volumes, Van Nostrand Reinhold, London, U.K.Google Scholar
  4. [8.4]
    Iain G. Currie (1974), Fundamental Mechanics of Fluids, McGraw–Hill, New York.zbMATHGoogle Scholar
  5. [8.5]
    John A. Duffle and William A. Beckman (1980), Solar Engineering of Thermal Processes, John Wiley, New York.Google Scholar
  6. [8.6]
    Hilding Elmqvist (1978), A Structured Model Language for Large Continuous Systems, Ph.D. dissertation, Report CODEN: LUTFD2/(TRFT-1015), Dept. of Automatic Control, Lund Institute of Technology, Lund, Sweden.Google Scholar
  7. [8.7]
    International Colloquium on Field Simulation (1976), Proceedings of the Fourth International Colloquium on the Beuken Model, September 1974, Polytechnic of Central London, London, U.K.Google Scholar
  8. [8.8]
    Aharon Katzir–Katchalsky and Peter F. Curran (1965), Nonequilibrium Thermodynamics in Biophysics, Harvard University Press, Cambridge, Mass.Google Scholar
  9. [8.9]
    Bernard H. Lavenda (1985), Nonequilibrium Statistical Thermodynamics, John Wiley, New York.zbMATHGoogle Scholar
  10. [8.10]
    Derek F. Lawden (1987), Principles of Thermodynamics and Statistical Mechanics, John Wiley, New York.Google Scholar
  11. [8.11]
    Fritz London (1954), Superfluids — Volume II: Macroscopic Theory of Superfluid Helium, John Wiley, New York.Google Scholar
  12. [8.12]
    Edward E. L. Mitchell and Joseph S. Gauthier (1986), ACSL: Advanced Continuous Simulation Language — User Guide and Reference Manual, Mitchell & Gauthier Assoc., Concord, Mass.Google Scholar
  13. [8.13]
    V. Peshkov (1944), “’Second Sound’ in Helium II,” J. Phys. USSR, 8, p. 381.Google Scholar
  14. [8.14]
    V. Peshkov (1946), “Determination of the Velocity of Propagation of the Second Sound in Helium II,” J. Phys. USSR, 10, pp. 389–398.Google Scholar
  15. [8.15]
    Ilya Prigogine (1967), Thermodynamics of Irreversible Processes, third edition, John Wiley Interscience, New York.Google Scholar
  16. [8.16]
    Ilya Prigogine (1980), From Being to Becoming: Time and Complexity in the Physical Sciences, Freeman, San Francisco, Calif. Homework Problems 333Google Scholar
  17. [8.17]
    Keith S. Stowe (1984), Introduction to Statistical Mechanics and Thermodynamics, John Wiley, New York.zbMATHGoogle Scholar
  18. [8.18]
    Jean U. Thoma (1975), “Entropy and Mass Flow for Energy Conversion,” J. Franklin Institute, 299 (2), pp. 89–96.CrossRefGoogle Scholar
  19. [8.19]
    Clifford Truesdell (1984), Rational Thermodynamics, second edition, Springer-Verlag, New York.CrossRefzbMATHGoogle Scholar
  20. [8.20]
    Y. L. Yao (1981), Irreversible Thermodynamics, Science Press, Beijing, distributed by Van Nostrand Reinhold, New York.Google Scholar


  1. [B8.1]
    Albert M. Bos and Peter C. Breedveld (1985), “Update of the Bond Graph Bibliography,” J. Franklin Institute, 319 (1/2), pp. 269–286.CrossRefzbMATHGoogle Scholar
  2. [B8.2]
    Peter C. Breedveld, Ronald C. Rosenberg, and T. Zhou (1991), “Bibliography of Bond Graph Theory and Application,” J. Franklin Institute, to appear.Google Scholar
  3. [B8.3]
    Vernon D. Gebben (1979), “Bond Graph Bibliography,” J. Franklin Institute, 308 (3), pp. 361–369.CrossRefzbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1991

Authors and Affiliations

  • François E. Cellier
    • 1
  1. 1.Department of Electrical and Computer Engineering and Applied Mathematics ProgramUniversity of ArizonaTucsonUSA

Personalised recommendations