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Transition state theory: A generalization to nonequilibrium systems with power-law distributions

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  • Du, Jiulin

Abstract

Transition state theory (TST) is generalized to nonequilibrium systems with power-law distributions. The stochastic dynamics that gives rise to the power-law distributions for the reaction coordinate and momentum is modeled by Langevin equations and corresponding Fokker–Planck equations. It is considered that a system far away from equilibrium does not have to relax to a thermal equilibrium state with Boltzmann–Gibbs distribution, but asymptotically approaches a nonequilibrium stationary state with a power-law distribution. Thus, we obtain a possible generalization of TST rates to nonequilibrium systems with power-law distributions. Furthermore, we derive the generalized TST rate constants for one-dimensional and n-dimensional Hamiltonian systems away from equilibrium, and obtain a generalized Arrhenius rate for systems with power-law distributions.

Suggested Citation

  • Du, Jiulin, 2012. "Transition state theory: A generalization to nonequilibrium systems with power-law distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(4), pages 1718-1728.
    • Handle: RePEc:eee:phsmap:v:391:y:2012:i:4:p:1718-1728
    DOI: 10.1016/j.physa.2011.11.009
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    Cited by:

    1. Tawfik, Ashraf M. & Elkamash, I.S., 2022. "On the correlation between Kappa and Lévy stable distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 601(C).

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