Abstract
A concept of separation of procedures is introduced to study cooperative phenomena theoretically. Some typical important examples of this concept are presented to clarify its usefulness; Kubo's stochastic Liouville equation, some generalized diffusionlike equations, van Kampen's expansion, Kubo's extensivity, Prigogine's entropy production, the scaling theory of transient phenomena based on the Lie algebra, and Suzuki's CAM theory of cooperative phenomena are discussed from the new viewpoint of separation of procedures.
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References
I. Prigogine,Introduction to Thermodynamics of Irreversible Processes (1967).
P. Glansdorff and I. Prigogine,Thermodynamic Theory of Structure, Stability and Fluctuations (Wiley-Interscience, New York, 1971).
G. Nicolis and I. Prigogine,Self-Organization in Nonequilibrium Systems (Wiley-Interscience, New York, 1977).
G. Nicolis, G. Dewel, and J. W. Turner, eds.,Order and Fluctuations in Equilibrium and Nonequilibrium Statistical Mechanics (Wiley, New York, 1981).
C. Domb and M. S. Green, eds.,Phase Transitions and Critical Phenomena.
M. Suzuki,Adv. Chem. Phys. 46:195 (1981).
M. Suzuki,Prog. Theor. Phys. (Suppl.) 69:160 (1980).
M. Suzuki,Prog. Theor. Phys. (Suppl.) 79:125 (1984).
T. Carleman,Acta Math. 59:63 (1932).
B. J. Alder and T. E. Wainwright,Phys. Rev. 127:359 (1962).
M. Suzuki,Prog. Theor. Phys. 56:77, 477 (1976).
M. Suzuki,J. Stat. Phys. 16:11, 477 (1977).
M. Suzuki,Physica 117A:193 (1983).
M. Suzuki,J. Math. Phys. 26:601 (1985).
M. Suzuki,Physica 138A:433 (1986).
R. Kubo,J. Math. Phys. 4:174 (1963).
R. Kubo,J. Phys. Soc. Jpn. 17:1100 (1962).
G. Rosen,Phys. Rev. Lett. 53:307 (1984).
R. Kubo, inSynergetics, H. Haken, ed. (B. G. Teubner, Stuttgart, 1973).
R. Kubo, K. Matsuo, and K. Kitahara,J. Stat. Phys. 9:51 (1973).
M. Suzuki,Prog. Theor. Phys. 52:1657 (1975).
M. Suzuki,Prog. Theor. Phys. 55:383 (1976).
N. G. van Kampen,Can. J. Phys. 39:551 (1961).
M. Suzuki,J. Stat. Phys. 14:129 (1976).
W. Magnus,Commun. Pure Appl. Math. 7:649 (1954).
J. Wei and E. Norman,Proc. Am. Math. Soc. 15:327 (1963);J. Math. Phys. 4:575 (1963).
R. M. Wilcox,J. Math. Phys. 8:962 (1967); see also M. Suzuki,Commun. Math. Phys. 51:183 (1976).
M. Suzuki,J. Phys. Soc. Jpn. 55:4205 (1986);Phys. Lett. 116A:375 (1986).
M. Suzuki, inQuantum Field Theory, F. Mancini, ed. (North-Holland, Amsterdam, 1986).
M. Suzuki and M. Katori,J. Phys. Soc. 55:1 (1986).
M. Suzuki, M. Katori, and X. Hu,J. Phys. Soc. 56:3092 (1987).
M. Katori and M. Suzuki,J. Phys. Soc. 56:3113 (1987).
X. Hu, M. Katori, and M. Suzuki,J. Phys. Soc. 56:3865 (1987).
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This paper is dedicated to Ilya Prigogine on the occasion of his 70th birthday.
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Suzuki, M. Nonlinear fluctuations, separation of procedures, and linearization of processes. J Stat Phys 49, 977–992 (1987). https://doi.org/10.1007/BF01017555
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DOI: https://doi.org/10.1007/BF01017555