Advertisement

Short History of Non-equilibrium Thermodynamics

  • Henry W. HaslachJr
Chapter

Abstract

Thermodynamics is intended to be a universal description of the world we live in. Thermodynamics began in the attempt to understand the cycles of the steam engine in the mid-nineteenth century in which the cycles were essentially considered quasi-static processes, those consisting of a sequence of equilibrium states. Most real processes, however, are non-equilibrium processes and therefore are time-dependent. They are dynamic, not quasi-static, and generally involve dissipation. Dissipation is common in natural phenomena including friction, permanent deformation of solids, release of heat, etc. and cannot be described by quasi-static or time reversible physics. But even so, the earliest researchers in the subject identified the first and second laws of thermodynamics. In the twentieth century, researchers began to describe non-equilibrium thermodynamic behavior, an effort that required reformulation of the second law, which, even if vague, is an attempt to ensure that, in the thermodynamic description, heat can only flow from hot to cold regions unless the process is forced. This chapter does not review in detail other thermodynamics theories, but rather identifies the issues and problems to be dealt with by the maximum dissipation non-equilibrium thermodynamic construction.

Keywords

Entropy Production Dissipation Function Internal State Variable Fading Memory Liapunov Function 
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.

References

  1. B. Bernstein (1960). Proof of Carathéodory’s local theorem and its global application to thermostatics. Journal of Mathematical Physics 1(3), 222–224.MathSciNetMATHCrossRefGoogle Scholar
  2. D. B. Bogy and P. M. Naghdi (1970). On heat conduction and wave propagation in rigid solids. Journal of Mathematical Physics 11, 917–923.MATHCrossRefGoogle Scholar
  3. R. M. Bowen (1989). Introduction to Continuum Mechanics for Engineers, Plenum Press, New York.MATHCrossRefGoogle Scholar
  4. R. W. Brockett (1983). Asymptotic stability and feedback stabilization. Differential Geometric Control Theory, Birkäuser, Boston, pp 181–191.MATHGoogle Scholar
  5. C. Carathéodory (1909). Investigations into the Foundations of Thermodynamics. In The Second Law of Thermodynamics, ed. J. Kestin, Dowden, Hutchinson and Ross Inc., Stroudsberg, PA, 1976. Originally, (Untersuchungen über die Grundlagen der Thermodynamik, Math. Ann. 67, 355–386).Google Scholar
  6. P. Cermelli, E. Fried and S. Sellers (2001). Configurational stress, yield and flow in rate independent plasticity. Proceedings of the Royal Society of London A 457, 1447–1467.MathSciNetMATHCrossRefGoogle Scholar
  7. R. M. Christensen (1982). Theory of Viscoelasticity; an introduction. 2nd Ed., Academic Press, New York.Google Scholar
  8. B. D. Coleman (1964). On thermodynamics, strain, impulses and viscoelasticity. Archive for Rational Mechanics and Analysis 17, 230–254.MathSciNetMATHGoogle Scholar
  9. B. D. Coleman and M. E. Gurtin (1967). Thermodynamics with internal state variables. Journal of Chemical Physics 47, 597–613.CrossRefGoogle Scholar
  10. Y. Demirel and S. I. Sandler (2001). Linear-nonequilibrium thermodynamics theory for coupled heat and mass transport. International Journal of Heat and Mass Transfer 44, 2439–2451.MATHCrossRefGoogle Scholar
  11. Y. Demirel and S. I. Sandler (2004). Nonequilibrium thermodynamics in engineering and science. Journal of Physical Chemistry B 108, 31–43.CrossRefGoogle Scholar
  12. L. Deseri and R. Mares (2000). A class of viscoplastic constitutive models based on the maximum dissipation principle. Mechanics of Materials 32, 389–403.CrossRefGoogle Scholar
  13. P. Duhem (1906). Recherches sur l’Elasticité. Gauthier-Villars, Paris.MATHGoogle Scholar
  14. P. Duhem (1911). Traité d’Enérgétique ou Thermodynamique Générale, Gauthier-illars, Paris.MATHGoogle Scholar
  15. J. L. Ericksen (1991). Introduction to the Thermodynamics of Solids, 1st Ed., Chapman-Hall, London.MATHGoogle Scholar
  16. F. D. Fischer and J. Svoboda (2007). A note on the principle of maximum dissipation rate. Journal of Applied Mechanics 74, 923–926.CrossRefGoogle Scholar
  17. L. S. Garcìa-Colìn (1988). Extended non-equilibrium thermodynamics, scope and limitations. Revista Mexicana de Fisica 34, 344–366.Google Scholar
  18. L. S. Garcìa-Colìn and F. J. Uribe (1991). Extended irreversible thermodynamics, beyond the linear regime: a critical overview. Journal of Non-Equilibrium Thermodynamics 16, 89–128.Google Scholar
  19. J. W. Gibbs (1873a). Graphical methods in the thermodynamics of fluids. In The Collected Works, Vol. 1, Yale University Press, New Haven, 1948.Google Scholar
  20. J. W. Gibbs (1873b). A method of geometrical representation of the thermodynamic properties of substances by means of surfaces. Transactions of the Connecticut Academy II, 382–404. Also in The Collected Works, Vol. 1, Yale University Press, New Haven 1948, 33–54.Google Scholar
  21. S. R. de Groot and P. Mazur (1984). Non-equilibrium Thermodynamics, Dover, New York.Google Scholar
  22. A. E. Green and P. M. Naghdi (1977). On thermodynamics and the nature of the second law. Proceedings of the Royal Society of London, Series A 357, 253–270.MathSciNetCrossRefGoogle Scholar
  23. M. E. Gurtin (1968). On the thermodynamics of materials with memory. Archive for Rational Mechanics and Analysis 28, 40–50.MathSciNetMATHCrossRefGoogle Scholar
  24. R. B. Hall (2008). Combined thermodynamics approach for anisotropic, finite deformation overstress models of viscoplasticity. International Journal of Engineering Science 46, 119–130.MathSciNetMATHCrossRefGoogle Scholar
  25. R. Hill (1948). A variational principle of maximum plastic work in classical plasticity, A. J. Mech. Applied Math. 1, 18–28.MATHCrossRefGoogle Scholar
  26. R. Hill (1958). A general theory of uniqueness and stability in elastic-plastic solids. Journal of the Mechanics and Physics of Solids 6, 236–249.MATHCrossRefGoogle Scholar
  27. G. A. Holzapfel (2000). Nonlinear Solid Mechanics, 2005 reprinting. Wiley, Chichester.MATHGoogle Scholar
  28. B. H. Lavenda (1993). Thermodynamics of Irreversible Processes, Dover, New York.Google Scholar
  29. J. Lubliner (1984). A maximum-dissipation principle in generalized plasticity. Acta Mechanica 52, 225–237.MathSciNetMATHCrossRefGoogle Scholar
  30. A. Lyapunov (1892). Problème general de la stabilité du mouvement. In Annual of Mathematics Studies 17, Princeton University Press (1949).Google Scholar
  31. J. Mandel (1973). Thermodynamics and Plasticity. In Foundations of Continuum Thermodynamics, ed. J. J. Delgado Domingos, M. N. R. Nina, J. H. Whitelaw, John Wiley and Sons, New York.Google Scholar
  32. L. M. Martyusheva and V. D. Seleznev (2006). Maximum entropy production principle in physics, chemistry and biology. Physics Reports 426, 1–45.MathSciNetCrossRefGoogle Scholar
  33. A. Moroz (2008). On a variational formulation of the maximum energy dissipation principle for non-equilibrium chemical thermodynamics. Chemical Physics Letters 457, 448–452.CrossRefGoogle Scholar
  34. I. Müller (1967). On the entropy inequality. Archive for Rational Mechanics and Analysis 26, 118–141.MathSciNetMATHCrossRefGoogle Scholar
  35. I. Müller and T. Ruggeri (1998). Rational Extended Thermodynamics, 2nd Ed., Springer, New York.MATHCrossRefGoogle Scholar
  36. Nguyen Quoc Son (1984). Bifurcation et stabilité des systèmes irréversibles obéissant au principe de dissipation maximale. Journal de Méchanique théorique et appliqué 3, 41–61.MATHGoogle Scholar
  37. L. Onsager (1931). Reciprocal relations in irreversible processes I, Physical Review 37, 405–426, and Reciprocal relations in irreversible processes II, Physical Review 38, 2265–2279.CrossRefGoogle Scholar
  38. M. Planck (1879). Über den zweiten Hauptsatz der mechanischen Wärmetheorie (Phd dissertation presented to the University of Munich).Google Scholar
  39. L. Pogliani and M. N. Berberan-Santos (2000). Constantin Carathéodory and the axiomatic thermodynamics. Journal of Mathematical Chemistry 28(1–3), 313–324.MathSciNetMATHCrossRefGoogle Scholar
  40. I. Prigogine and R. Defay (1954). Chemical Thermodynamics, Chapter IV, translated by D.H. Everett, Longmans, Green & Co.Google Scholar
  41. J. Serrin (1986). An outline of thermodynamical structure. In New Perspectives in Thermodynamics, ed. J. Serrin, Springer-Verlag, Berlin.CrossRefGoogle Scholar
  42. C. Truesdell (1984). Rational Thermodynamics, Springer Verlag, New York.MATHCrossRefGoogle Scholar
  43. C. Truesdell and R. A. Toupin (1960). The Classical Field Theories. Handbuch der Physik Vol. III/1, Ed. S. Flugge, Springer-Verlag, Berlin, Sec. 293.Google Scholar
  44. F. W. Wilson (1966). The structure of the level surfaces of a Lyapunov function. Journal of Differential Equations 3, 323–329.CrossRefGoogle Scholar
  45. Q. Yang, L. G. Tham, and G. Swoboda (2005). Normality structures with homogeneous kinetic rate laws. Journal of Applied Mechanics 72, 322–329.MATHCrossRefGoogle Scholar
  46. H. Ziegler and C. Wehrli (1987). On a principle of maximum rate of entropy production. Journal of Non-equilibrium Thermodynamics 12, 229–243.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringUniversity of MarylandCollege ParkUSA

Personalised recommendations