Abstract
A theory of fluctuations of macrovariables in nonequilibrium systems based on a nonlinear master equation is outlined. This equation takes into account, via a “mean field” type of approximation, the effect of the spatial extension of fluctuations. A comparison with the birth and death formalism reveals several unsatisfactory features of the latter.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
L. D. Landau and E. M. Lifshitz,Statistical Physics, Pergamon Press, Oxford (1959).
D. Massignon,Mécanique Statistique des Fluides, Dunod, Paris (1957).
G. Nicolis and I. Prigogine,Proc. Nat. Acad. Sci. (U.S.A.) 68:2102 (1971).
G. Nicolis, M. Malek-Mansour, K. Kitahara, and A. Van Nypelseer,Phys. Lett. 48A:217 (1974).
M. Bartlett,Stochastic Population Models in Ecology and Epidemiology, Meth. Mon. in Appl. Prob, and Stat. (1960).
G. Nicolis and I. Prigogine, inProc. Faraday Symposium 9 on the Physical Chemistry of Oscillatory Phenomena, The Royal Institution, London, (December 1974).
D. McQuarrie,Suppl. Rev. Series in Appl. Prob., Methuen, London (1967).
G. Nicolis and A. Babloyantz,J. Chem. Phys. 51:2632 (1969).
R. Hawkins and S. A. Rice,J. Theor. Biol. 30:579 (1971).
G. Nicolis,J. Stat. Phys. 6:195 (1972).
G. Nicolis, P. Allen, and A. Van Nypelseer,Progr. Theor. Phys. 52:481 (1974).
N. Saito,J. Chem. Phys. 61:3644 (1974).
Y. Kuramoto,Progr. Theor. Phys. 49:1782 (1973).
A. Nitzan and J. Ross,J. Stat. Phys. 10:379 (1974).
R. Mazo,J. Chem. Phys., in press.
G. Nicolis, inCooperative Phenomena, H. Haken, ed., North-Holland, Amsterdam (1974).
I. Prigogine, G. Nicolis, R. Herman, and T. Lam,Cooperative Phenomena 2:1 (1974).
Y. Kuramoto,Progr. Theor. Phys. 52:711 (1974).
A. Nitzan, P. Ortoleva, and J. Ross, inProc. Faraday Symposium 9 on the Physical Chemistry of Oscillatory Phenomena, The Royal Institution, London (December 1974).
M. Franckson, Mémoire de Licence, Univ. of Brussels (1975).
S. Chapman and T. G. Cowling,The Mathematical Theory of Non-uniform Gases, Cambridge Univ. Press, Cambridge (1960).
I. Prigogine and R. Herman,Statistical Theory of Vehicular Traffic, Elsevier, New York (1971).
D. Widom,Physica 73:107 (1974); K. G. Wilson,Physica 73:119 (1974).
H. P. McKean, inLecture Series in Differential Equations, Vol. II, Van Nostrand, Princeton, New Jersey (1969).
A. Erdélyiet al., eds.,Higher Transcendental Functions, Bateman Manuscript Project Vol. I, McGraw-Hill, New York (1953).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Malek-Mansour, M., Nicolis, G. A master equation description of local fluctuations. J Stat Phys 13, 197–217 (1975). https://doi.org/10.1007/BF01012838
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01012838