Abstract
We study fluctuations around nonequilibrium steady states of some model nonlinear chemical systems. A previous result of Nicolis and Prigogine states that the mean square fluctuation computed from a master equation in the space of internal states of the reacting species is identical to that calculated from Einstein's fluctuation formula. Our analysis of fluctuations based on that master equation leads with the assumption of local equilibrium to a result identical to that obtained from a master equation for the total concentration of the reacting species, which is different from the equilibrium (Einstein relation) result. Nicolis and Prigogine approximated one term in their master equation, and a discussion of this approximation is presented. The master equation without this approximation yields at equilibrium the result expected on the basis of Einstein's formula.
Similar content being viewed by others
References
D. M. McQuarrie,Adv. Chem. Phys. XV:149 (1969).
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 and I. Prigogine,Proc. Nat. Acad. Sci. U.S. 68:2102 (1971).
P. Glansdorff and I. Prigogine,Thermodynamic Theory of Structure, Stability and Fluctuations, Wiley, London (1971).
M. Lax,Rev. Mod. Phys. 32:25 (1960).
M. Lax,Rev. Mod. Phys. 38:359 (1966).
Y. Kuramoto,Prog. Theor. Phys. 49:1782 (1973).
Author information
Authors and Affiliations
Additional information
Work supported in part by the National Science Foundation and Project SQUID, Office of Naval Research.
Rights and permissions
About this article
Cite this article
Nitzan, A., Ross, J. A comment on fluctuations around nonequilibrium steady states. J Stat Phys 10, 379–390 (1974). https://doi.org/10.1007/BF01008800
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01008800