Abstract
We study, using master equation techniques, the time evolution of the average concentration and fluctuations in the two-speciesn-molecule reactionA+(n-1)X⇌nX in one dimension described by a Glauber-type dynamical lattice model for the specific casesn=2 (bimolecular) andn=3 (trimolecular). The evolution is found to be quite different from that described by the Mean-Field equations even for the bimolecular case, where the steady state is meanfield. For the trimolecular process, the values of fluctuation correlations in the nonequilibrium steady state are well predicted by the fixed points of the dynamical equations obtained from the master equation. In addition, three-point fluctuation correlations are found to play an important role in both processes and are accounted for by an extended Bethe-type ansatz. The bimolecular system shows no memory effects of initial conditions, while the trimolecular system is characterized by memory effects in terms of the average concentration, fluctuations as well as the entropy. The spatial decay of fluctuation correlations is found to be short range at the steady state for the trimolecular system.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
G. Nicolis and I. Prigogine,Self-Organization in Nonequilibrium Systems (Wiley, New York, 1977); H. Malchow and L. Schimansky-Gei,Noise and Diffusion in Bistable Nonequilibrium Systems (B. G. Teubner Verlagsgeselleschaft, 1985).
S.-K. Ma,Modern Theory of Critical Phenomena (Benjamin, New York, 1976); H. E. Stanley,Introduction to Phase Transitions and Critical Phenomena (Oxford University Press, Oxford, 1971).
G. H. Weiss and R. J. Rubin,Adv. Chem. Phys. 52:363 (1983); S. Havlin and D. ben-Avraham,Adv. Phys. 36:695 (1987).
G. Nicolis and M. Malek Mansour,J. Stat. Phys. 22:495 (1980); M. Malek Mansour, C. van den Broeck, G. Nicolis, and J. W. Turner,Ann. Phys. (N. Y.)131:283 (1981); P. Grassberger,Z. Phys. B 47:365 (1982).
R. J. Glauber,J. Math. Phys. 4:294 (1963).
A. Provata, J. W. Turner, and G. Nicolis,J. Stat. Phys. 70:1195 (1993).
A. Tretyakov, A. Provata, and G. Nicolis,J. Phys. Chem. 99:2770 (1994).
K. Kaneko,Physica D 34:1 (1989).
M. Malzek Mansour and J. Houard,Phys. Lett. 70 A:366 (1979); J. Houard, Mémoire, Université Libre de Bruxelles (1978).
G. Nicolis and M. Malek-Mansour,Prog. Theor. Phys. (Suppl.) 64:249 (1978).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Prakash, S., Nicolis, G. Dynamics of fluctuations in a reactive system of low spatial dimension. J Stat Phys 82, 297–322 (1996). https://doi.org/10.1007/BF02189232
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF02189232