Nonlinear Networks and Onsager–Casimir Reversibility

IEEE Transactions on Circuits and Systems

Volumn 27, Issue 11, 1980, Pages 1051-1058

  Anderson, Brian D O ^a  

^a UNIVERSITY OF NEWCASTLE   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

ELECTRIC NETWORKS, NONLINEAR;

EID: 0019079308     PISSN: 00984094     EISSN: None     Source Type: Journal    
DOI: 10.1109/TCS.1980.1084744     Document Type: Article

References (25)

1. J. Meixner, “Network theory in its relation to thermodynamics,” in Proc. Symp. on Generalized Networks, (Polytechnic Institute of Brooklyn, NY) pp. 13-25, 1966.
2. R. W. Brockett and J. C. Willems, “Stochastic control and the second law of thermodynamics,” in Proc. 1978 Decision and Control Conference, (San Diego, CA), pp. 1007-1011.
3. H. Nyquist, “Thermal agitation of electrical charge in conductors,” Phys. Rev., vol. 32, no. 1, pp. 110-173, 1928.
4. H. B. Callen and R. F. Greene, “On a theorem of irreversible thermodynamics,” Phys. Rev., vol. 86, no. 5, pp. 702-710, 1952.
5. H. B. G. Casimir, “On Onsager's principle of microscopic reversibility,” Rev. Mod. Phys., vol. 17, pp. 343-350, 1945.
6. “Reciprocity theorems and irreversible processes,” Proc. IEEE, vol. 51, pp. 1570-1583, 1963.
7. J. Meixner, “Thermodynamics of electrical networks and the Onsager-Casimir reciprocal relations,” J. Math. Phys., vol. 4, no. 2, pp. 154-159, 1963.
8. B. D. O. Anderson and T. Kailath, “Forwards, backwards and dynamically reversible Markovian models of second-order processes,” IEEE Trans. Circuits Syst., to appear.
9. J. C. Willems, “Time Reversibility in Deterministic and Stochastic Dynamical Systems,” in Proc. 1977 U. S.-Italy Seminar on Variable Structure Systems', Springer Lecture Notes in Economics and Mathematical Systems, to appear.
10. S. R. de Groot, “On the development of nonequilibrium thermodynamics,” J. Math. Phys., vol. 4, no. 2, pp. 147-153, 1963.
11. S. R. de Groot and P. Mazur, Nonequilibrium Thermodynamics, Amsterdam, The Netherlands: North-Holland, 1962.
12. N. G. Van Kampen, “Exact calculation of the fluctuation spectrum of a nonlinear model system,” J. Math. Phys., vol. 2, no. 4, pp. 592-601, 1961.
13. D. K. C. MacDonald, “The Brownian movement of linear and nonlinear systems,” Phil. Mag., vol. 45, no. 360, pp. 63-72, 1954.
14. C. T. J. Alkemade, “On the problem of Brownian motion of nonlinear systems,” Physica, vol. 24, pp. 1029-1034, 1958.
15. N. G. Van Kampen, “Nonlinear thermal fluctuations in a diode,” Physica, vol. 26, pp. 585-604, 1960.
16. W. Bernard and H. B. Callen, “Irreversible thermodynamics of a nonlinear RC system,” Phys. Rev., vol. 118, no. 6, pp. 1466-1470, 1960.
17. G. Oster, A. Perelson, and A. Katchalsky, “Network thermodynamics,” Nature, vol. 234, pp. 393-399, 1971.
18. 1.1. Gihman and A. V. Skorohod, Stochastic Differential Equations. Berlin, Springer, 1972.
19. B. D. O. Anderson, “Reverse-time diffusion equation models,” Stochastic Processes and Their Applications, to appear.
20. R. S. Palais, “Natural operations on differential forms,” Trans. Amer. Math. Soc., vol. 92, pp. 125-141, 1959.
21. L. O. Chua and Y. F. Lam, “A theory of algebraic n-ports,” IEEE Trans. Circuit Theory, vol. 20, no. 4, pp. 370-381, 1973.
22. C. Cherry, “Some general theorems for nonlinear systems possessing reactance,” Phil. Mag., vol. 42, no. 333, pp. 1161-1177, 1951.
23. R. K. Brayton and J. K. Moser, “A theory of nonlinear networks, I and II,” Quart. Appl. Math., vol. 3, no. 2, pp. 1-33, pp. 81-104, 1964.
24. N. T. Hung and B. D. O. Anderson, “Analysis and synthesis of nonlinear reciprocal networks containing two element types and transformers,” IEEE Trans. Circuits Syst., to appear.
25. L. D. Landau and E. M. Lifschitz, Statistical Physics. Pergamon, Oxford, 1969.