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
Onsager, L., Phys. Rev., 37, 405 (1931); 38, 2265 (1931).
Prigogine, I., Etude Thermodynamique des Processus Irreversibles (Desoer, Liège, 1947).
Meixner, J., Ann. Physik, 39, 333 (1941), 40, 165 (1941), 41, 409 (1942), 43, 244 (1943).
de Groot, S. R., Thermodynamics of Irreversible Processes (Inter-science Publishers, New York, 1951).
Meixner, J., in Symposium on Generalized Networks, 16 (Polytechnic Press of the Polytechnic Institute of Brooklyn, Brooklyn, New York, 1966).
Sudarshan, E. C. G., The Structure of Dynamical Theories Brandeis Lectures, 1962, 2 (W. A. Benjamin, Inc., New York, 1963).
Branin, F., Symposium on Generalized Networks, IBM Tech. Rept. TROO. 855, 16 (Polytechnic Press of the Polytechnic Institute of Brooklyn, Brooklyn, New York, 1966).
Hocking, J., and Young, G., Topology (Addison-Wesley, Reading, Mass., 1961).
Kron, G., Elec Eng., 67, 672 (1948).
Kron, G., Phys. Rev., 64, 126 (1943).
Kron, G., J. Aeron. Sci., 12, 221 (1945).
Kron, G., J. Chem. Phys., 14, 19 (1946).
Trent, H. M., J. Acoustic Soc. Amer., 27, 500 (1955).
Olson, H., Dynamical Analogies, second ed. (D. Van Nostrand, Princeton, New Jersey, 1958).
Finkelstein, A., and Mauro, A., Biophys. J., 3, 215 (1963).
Cole, K., Membranes, Ions and Impulses (Univ. of California Press, Berkeley, 1968).
Penfield, P., and Haus, H., Electrodynamics of Moving Media (MIT Press, Cambridge, Mass., 1967).
Rohrer, R., Circuit Theory: The State Space Approach (McGraw-Hill, New York, 1970).
Shearer, J., Murphy, A. T., and Rechardson, H. H., Introduction to System Dynamics (Addison-Wesley, Reading, Mass., 1967).
Koenig, H., Tokad, Y., and Kesavan, H. K., Analysis of Discrete Physical Systems (McGraw-Hill, New York, 1969).
Martens, H., and Allen, D., Introduction to Systems Theory (Merrill, Columbus, Ohio, 1969).
Paynter, H., Analysis and Design of Engineering Systems (MIT, Cambridge, Mass., 1961).
Karnopp, D., and Rosenberg, R., Analysis and Simulation of Multiport Systems (MIT, Cambridge, Mass., 1968).
Oster, G., and Auslander, D., Topological Representations of Thermodynamic Systems (J. Franklin Institute, in the press, 1971).
Oster, G., Perelson, A., and Katchalsky, A., Thermodynamics of Biological Networks (Quart. Rev. Biophys., in the press, 1971).
Brayton, R. K., IBM Report RC 2606 (No. 12927), Sept. 1969; Quart. Appl. Maths., 22, 1 (1964), 22, 81 (1964).
Desoer, C., and Kuh, E., Basic Circuit Theory (McGraw-Hill, New York, 1969).
Katchalsky, A., and Curran, P. F., Nonequilibrium Thermodynamics in Biophysics (Harvard University Press, Cambridge, Mass., 1965).
Kirkwood, J. G., Ion Transport Across Membranes (edit. by Clark, H. T.), 119–122 (Academic Press New York, 1964).
Spiegler, K., Trans. Faraday Soc., 429, part 9 (1958).
Kedem, O., and Katchalsky, A., J. Gen. Physiol., 45, 143 (1961).
Tellegen, B. D., Phillips Res. Rept., 7, 259 (1952).
Oster, G., and Desoer, C. A., Tellegen's Theorem and Thermodynamic Inequalities, J. Theor. Biol., 32, 219 (1971).
Penfield, P., Tellegen's Theorem (MIT, Cambridge, Mass., 1970).
Bers, A. and Penfield, P., IRE Trans. ED-9, 12 (1962).
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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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DOI: https://doi.org/10.1038/234393a0
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