Quasi-Thermodynamic Kinetic Systems

  • Martin Feinberg
Part of the Applied Mathematical Sciences book series (AMS, volume 202)


In Chapter 7 we discussed, briefly, origins of the Deficiency Zero Theorem. There we introduced the idea of complex balancing, a major generalization by Horn and Jackson [109] of an earlier related idea, detailed balancing. We also hinted at connections of both ideas to classical thermodynamics. In this chapter we will elaborate on thermodynamic roots underlying arguments to come, largely to provide motivation for purely mathematical proof techniques that might otherwise seem improvisatory.


  1. 29.
    Bowen, R.M.: Thermochemistry of reacting materials. The Journal of Chemical Physics 49(4), 1625–1637 (1968)CrossRefGoogle Scholar
  2. 40.
    Coleman, B.D., Noll, W.: The thermodynamics of elastic materials with heat conduction and viscosity. Archive for Rational Mechanics and Analysis 13(1), 167–178 (1963)MathSciNetCrossRefGoogle Scholar
  3. 55.
    Deng, J., Jones, C., Feinberg, M., Nachman, A.: On the steady states of weakly reversible chemical reaction networks. arXiv:1111.2386 [physics, q-bio] (2011)Google Scholar
  4. 62.
    Ellison, P., Ji, H., Knight, D., Feinberg, M.: The Chemical Reaction Network Toolbox, Version 2.3 (2014). Available at
  5. 69.
    Feinberg, M.: Constitutive equations for ideal gas mixtures and ideal solutions as consequences of simple postulates. Chemical Engineering Science 32(1), 75–78 (1977)CrossRefGoogle Scholar
  6. 71.
    Feinberg, M.: Lectures on Chemical Reaction Networks (1979). Written version of lectures given at the Mathematical Research Center, University of Wisconsin, Madison, WI Available at
  7. 76.
    Feinberg, M.: The existence and uniqueness of steady states for a class of chemical reaction networks. Archive for Rational Mechanics and Analysis 132(4), 311–370 (1995)MathSciNetCrossRefGoogle Scholar
  8. 81.
    Feinberg, M., Lavine, R.: Thermodynamics based on the Hahn-Banach theorem: the Clausius inequality. Archive for Rational Mechanics and Analysis 82(3), 203–293 (1983)MathSciNetCrossRefGoogle Scholar
  9. 82.
    Feinberg, M., Lavine, R.: Foundations of the Clausius-Duhem inequality. In: J. Serrin (ed.) New Perspectives in Thermodynamics, pp. 49–64. Springer, New York (1986). Also available at and as Appendix 2A in Truesdell, C., Rational Thermodynamics, Springer (1984)Google Scholar
  10. 98.
    Greub, W.H.: Linear Algebra, 4th edn. Springer, New York (1981)zbMATHGoogle Scholar
  11. 104.
    Hirsch, M.W., Smale, S., Devaney, R.L.: Differential Equations, Dynamical Systems, and an Introduction to Chaos, Third Edition. Academic Press (2012)zbMATHGoogle Scholar
  12. 109.
    Horn, F., Jackson, R.: General mass action kinetics. Archive for Rational Mechanics and Analysis 47(2), 81–116 (1972)MathSciNetCrossRefGoogle Scholar
  13. 119.
    Krambeck, F.J.: The mathematical structure of chemical kinetics in homogeneous single-phase systems. Archive for Rational Mechanics and Analysis 38(5), 317–347 (1970)MathSciNetCrossRefGoogle Scholar
  14. 143.
    Rockafellar, R.T.: Convex Analysis. Princeton University Press, Princeton, NJ (1996)Google Scholar
  15. 163.
    Stoer, J., Witzgall, C.: Convexity and Optimization in Finite Dimensions I. Springer, New York (2012)zbMATHGoogle Scholar
  16. 171.
    Wegscheider, R.: Über simultane gleichgewichte und die beziehungen zwischen thermodynamik und reactionskinetik homogener systeme. Monatshefte für Chemie und verwandte Teile anderer Wissenschaften 22(8), 849–906 (1901)CrossRefGoogle Scholar

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Authors and Affiliations

  • Martin Feinberg
    • 1
  1. 1.Chemical & Biomolecular Engineering, The Ohio State UniversityColumbusUSA

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