Abstract
The main result of this paper is a derivation of a generalized nonlinear Langevin equation (GLE) forn interacting particles in a bath. A consequence of the derivation is that the exact form of the (generalized) fluctuation-dissipation theorem is obtained. We discuss also the relation between the memory kernel of the GLE and some corresponding correlation functions which can be easily obtained in a molecular dynamics computer experiment. In the same spirit it is shown that the approach applies to a Brownian particle subjected to a stationary external field. The technique presented in a previous paper to simulate generalized Brownian dynamics can be easily extended to the present case. Our derivation intends to clarify the uses and (possibly) abuses of the Langevin equation in Brownian dynamics studies.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
P. Turq, F. Lantelme, and H. L. Friedman,J. Chem. Phys. 66:3039 (1977).
D. L. Ermak and J. A. McCammon,J. Chem. Phys. 69:1352 (1978).
D. Ceperley, M. M. Kalos, and J. Lebowitz,Phys. Rev. Lett. 41:313 (1978).
R. M. Levy, M. Karplus, and J. A. McCammon,Chem. Phys. Lett. 65:4 (1979).
E. Helfand,J. Chem. Phys. 69:1010 (1978).
A. Diebold, S. A. Adelman, and Y. Mou,J. Chem. Phys. 71:3236 (1979).
M. Shugard, J. Tully, and A. Nitzan,J. Chem. Phys. 64:336 (1978);
A. Nitzan, M. Shugard, and J. Tully,J. Chem. Phys. 64:2525 (1978).
M. R. Pear and J. H. Weiner,J. Chem. Phys. 69:785 (1978).
S. A. Adelman,J. Chem. Phys. 71:4471 (1979).
G. Ciccotti and J. P. Ryckaert,Mol. Phys.,40: 141 (1980).
B. J. Berne, ed.,Modem Theoretical Chemistry, Vol. 6,Statistical Mechanics, Part B: Time-dependent Processes (Plenum Press, New York, 1977).
H. Mori,Progr. Theor. Phys. 33:423 (1965);
H. Mori,Progr. Theor. Phys. 34:399 (1965).
J. M. Deutch and I. Oppenheim,J. Chem. Phys. 54:3547 (1971).
T. J. Murphy and J. L. Aguirre,J. Chem. Phys. 57:2098 (1972).
G. Wilemski,J. Stat. Phys. 14:153 (1976).
D. Chandler and L. R. Pratt,J. Chem. Phys. 65:2925 (1976).
R. Kubo,Rep. Prog. Phys. 29:255 (1966).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Ciccotti, G., Ryckaert, J.P. On the derivation of the generalized Langevin equation for interacting Brownian particles. J Stat Phys 26, 73–82 (1981). https://doi.org/10.1007/BF01106787
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01106787