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Network Thermodynamics

Abstract

The techniques of network theory are generalized to include irreversible thermodynamic systems. Complex nonlinear systems can be treated in this way in terms of a well-defined mathematical structure.

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References

  1. Onsager, L., Phys. Rev., 37, 405 (1931); 38, 2265 (1931).

    Article  ADS  CAS  Google Scholar 

  2. Prigogine, I., Etude Thermodynamique des Processus Irreversibles (Desoer, Liège, 1947).

    Google Scholar 

  3. Meixner, J., Ann. Physik, 39, 333 (1941), 40, 165 (1941), 41, 409 (1942), 43, 244 (1943).

    Article  ADS  CAS  Google Scholar 

  4. de Groot, S. R., Thermodynamics of Irreversible Processes (Inter-science Publishers, New York, 1951).

    MATH  Google Scholar 

  5. Meixner, J., in Symposium on Generalized Networks, 16 (Polytechnic Press of the Polytechnic Institute of Brooklyn, Brooklyn, New York, 1966).

    Google Scholar 

  6. Sudarshan, E. C. G., The Structure of Dynamical Theories Brandeis Lectures, 1962, 2 (W. A. Benjamin, Inc., New York, 1963).

    Google Scholar 

  7. Branin, F., Symposium on Generalized Networks, IBM Tech. Rept. TROO. 855, 16 (Polytechnic Press of the Polytechnic Institute of Brooklyn, Brooklyn, New York, 1966).

    Google Scholar 

  8. Hocking, J., and Young, G., Topology (Addison-Wesley, Reading, Mass., 1961).

    MATH  Google Scholar 

  9. Kron, G., Elec Eng., 67, 672 (1948).

    Article  MathSciNet  Google Scholar 

  10. Kron, G., Phys. Rev., 64, 126 (1943).

    Article  ADS  Google Scholar 

  11. Kron, G., J. Aeron. Sci., 12, 221 (1945).

    Article  MathSciNet  Google Scholar 

  12. Kron, G., J. Chem. Phys., 14, 19 (1946).

    Article  ADS  CAS  Google Scholar 

  13. Trent, H. M., J. Acoustic Soc. Amer., 27, 500 (1955).

    Article  ADS  Google Scholar 

  14. Olson, H., Dynamical Analogies, second ed. (D. Van Nostrand, Princeton, New Jersey, 1958).

    Google Scholar 

  15. Finkelstein, A., and Mauro, A., Biophys. J., 3, 215 (1963).

    Article  CAS  Google Scholar 

  16. Cole, K., Membranes, Ions and Impulses (Univ. of California Press, Berkeley, 1968).

    Google Scholar 

  17. Penfield, P., and Haus, H., Electrodynamics of Moving Media (MIT Press, Cambridge, Mass., 1967).

    Google Scholar 

  18. Rohrer, R., Circuit Theory: The State Space Approach (McGraw-Hill, New York, 1970).

    MATH  Google Scholar 

  19. Shearer, J., Murphy, A. T., and Rechardson, H. H., Introduction to System Dynamics (Addison-Wesley, Reading, Mass., 1967).

    Google Scholar 

  20. Koenig, H., Tokad, Y., and Kesavan, H. K., Analysis of Discrete Physical Systems (McGraw-Hill, New York, 1969).

    Google Scholar 

  21. Martens, H., and Allen, D., Introduction to Systems Theory (Merrill, Columbus, Ohio, 1969).

    Google Scholar 

  22. Paynter, H., Analysis and Design of Engineering Systems (MIT, Cambridge, Mass., 1961).

    Google Scholar 

  23. Karnopp, D., and Rosenberg, R., Analysis and Simulation of Multiport Systems (MIT, Cambridge, Mass., 1968).

    Google Scholar 

  24. Oster, G., and Auslander, D., Topological Representations of Thermodynamic Systems (J. Franklin Institute, in the press, 1971).

    Google Scholar 

  25. Oster, G., Perelson, A., and Katchalsky, A., Thermodynamics of Biological Networks (Quart. Rev. Biophys., in the press, 1971).

    Google Scholar 

  26. Brayton, R. K., IBM Report RC 2606 (No. 12927), Sept. 1969; Quart. Appl. Maths., 22, 1 (1964), 22, 81 (1964).

    Article  MathSciNet  Google Scholar 

  27. Desoer, C., and Kuh, E., Basic Circuit Theory (McGraw-Hill, New York, 1969).

    Google Scholar 

  28. Katchalsky, A., and Curran, P. F., Nonequilibrium Thermodynamics in Biophysics (Harvard University Press, Cambridge, Mass., 1965).

    Book  Google Scholar 

  29. Kirkwood, J. G., Ion Transport Across Membranes (edit. by Clark, H. T.), 119–122 (Academic Press New York, 1964).

    Google Scholar 

  30. Spiegler, K., Trans. Faraday Soc., 429, part 9 (1958).

  31. Kedem, O., and Katchalsky, A., J. Gen. Physiol., 45, 143 (1961).

    Article  CAS  Google Scholar 

  32. Tellegen, B. D., Phillips Res. Rept., 7, 259 (1952).

    MathSciNet  Google Scholar 

  33. Oster, G., and Desoer, C. A., Tellegen's Theorem and Thermodynamic Inequalities, J. Theor. Biol., 32, 219 (1971).

    CAS  PubMed  Google Scholar 

  34. Penfield, P., Tellegen's Theorem (MIT, Cambridge, Mass., 1970).

    Google Scholar 

  35. Bers, A. and Penfield, P., IRE Trans. ED-9, 12 (1962).

Download references

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OSTER, G., PERELSON, A. & KATCHALSKY, A. Network Thermodynamics. Nature 234, 393–399 (1971). https://doi.org/10.1038/234393a0

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