Abstract
The scope of the thermodynamic theory of nonlinear irreversible processes is widened to include the nonlinear stability analysis of system motion. The emphasis is shifted from the analysis of instantaneous energy flows to that of the average work performed by periodic nonlinear processes. The principle of virtual work separates dissipative and conservative forces. The vanishing of the work of conservative forces determines the natural period of oscillation. Stability is then determined by the variations of the dissipative forces with amplitude of oscillation. If the work is a minimum, under certain conditions, the motion is stable. Reduction to linear analysis shows the coincidence with the impedance analysis of electrical circuit theory. The theory is applied to the analysis of temporal interactions of nonlinear irreversible processes in the particular cases of synchronization and hysteresis. Characteristic nonequilibrium phenomena of directional energy transfers, self-excitation, system passivity, wave modulation, and “beat” phenomena are observed. Possible relationships with biological processes are discussed.
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References
B. H. Lavenda,Found. Phys. 2 (2/3), 161 (1972).
M. Herschowitz-Kaufman and G. Nicolis,J. Chem. Phys. 56, 1890 (1972).
C. Lanczos,The Variational Principles of Mechanics (Univ. of Toronto Press, Toronto, 1952), p. 74ff.
E. A. Guillemin,Introductory Circuit Theory (John Wiley and Sons, New York, 1953).
N. Minorsky,Nonlinear Oscillations (Van Nostrand, Princeton, N. J., 1942).
N. Minorsky,Theory of Nonlinear Control Systems (McGraw-Hill Book Co., New York, 1969).
N. Minorsky,Introduction to Nonlinear Mechanics (J. W. Edwards, Inc., Ann Arbor, Mich., 1947).
A. W. Langill, Jr.,Automatic Control Systems Engineering, Vol. 1 (Prentice Hall, Englewood Cliffs, N. J., 1965), p. 17.
Y. Rocard,General Dynamics of Vibrations (Crosby Lockwood and Son, London, 1960).
N. N. Bogolivbov and Y. A. Mitropolsky,Asymptotic Methods in the Theory of Nonlinear Oscillations (Hindustan Pub. Corp., Delhi, India, 1961), p. 338ff.
L. Mirsky,Introduction to Linear Algebra (Oxford Univ. Press, New York, 1955).
B. Van der Pol,Phil. Mag. 43 (April 1922).
B. H. Lavenda, in preparation.
B. C. Goodwin, inSymp. of the Soc. for General Microbiology XIX, 1969.
B. H. Lavenda, G. Nicolis, and M. Herschowitz-Kaufman,Theoret. Biol. 32, 28 (1971).
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Lavenda, B.H. Thermodynamics of nonlinear, interacting irreversible processes. II. Found Phys 3, 53–88 (1973). https://doi.org/10.1007/BF00708600
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DOI: https://doi.org/10.1007/BF00708600