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

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