Abstract
Two incarnations of the canonical ensemble probability distribution based on the generalization of statistical mechanics of Tsallis are described. A generalization of the law of mass action is used to derive equilibrium constants. Reaction rate constants for barrier crossing are derived using the transition state theory approximation. Monte Carlo and Molecular Dynamics algorithms which can be used to sample Tsallis statistical distributions are defined. The results are used to demonstrate that MC and MD algorithms which sample the Tsallis statistical distributions can be expected to enhance the rate of phase space sampling in simulations of many body systems.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
C. Tsallis. J. Stat Phys., 52: 479, 1988.
E.M.F. Curado and C. Tsallis. J. Phys. A: Math. Gen, 24: L69, 1991.
C. Tsallis. Phys. Rev. Lett, 75: 3589, 1995.
J. Maddox. Nature, 365: 103, 1993.
I. Andricioaei and J. E. Straub. Phys. Rev. E, E 53: R3055, 1996.
I. Andricioaei and J. E. Straub. J. Chem. Phys., 107: 9117, 1997.
B. J. Berne and J. E. Straub. Curr. Opin. Struc. Bio., 7: 181, 1997.
S. Huo and J.E. Straub. J. Chem. Phys., 107: 5000, 1993.
R. Zwanzig. J. Chem. Phys., 103: 9397, 1995.
Such “global” master equations have recently gained attention in the study of protein folding. See for example C. De Dominicis, H. Orland and F. Lainee, J. Phys. Lett, 46: L463, 1985; E.I. Shakhnovich and A. M. Gutin, Eurphys. Lett, 9: 569, 1989; J. G. Saven, J. Wang and P. G. Wolynes, J. Chem. Phys., 101:11037, 1994.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1999 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Straub, J.E., Andricioaei, I. (1999). Exploiting Tsallis Statistics. In: Deuflhard, P., Hermans, J., Leimkuhler, B., Mark, A.E., Reich, S., Skeel, R.D. (eds) Computational Molecular Dynamics: Challenges, Methods, Ideas. Lecture Notes in Computational Science and Engineering, vol 4. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-58360-5_11
Download citation
DOI: https://doi.org/10.1007/978-3-642-58360-5_11
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-63242-9
Online ISBN: 978-3-642-58360-5
eBook Packages: Springer Book Archive