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

Abstract

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.

19 pages

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• Are power-law distributions an equilibrium distribution or a stationary nonequilibrium distribution?
• The nonextensive statistical ensembles with dual thermodynamic interpretations
• The precise time-dependent solution of the Fokker-Planck equation with anomalous diffusion
• The mean first passage time in an energy-diffusion controlled regime with power-law distributions
• Escape rate for the power-law distribution in low-to-intermediate damping
• Power-law behaviors from the two-variable Langevin equation: Ito's and Stratonovich's Fokker-Planck equations
• Chain of kinetic equations for the distribution functions of particles in simple liquid taking into account nonlinear hydrodynamic fluctuations
• The power-law TST reaction rate coefficient with tunneling correction
• The collision frequency of electron-neutral-particle in the weakly ionized plasma with the power-law velocity distribution
• The power-law reaction rate coefficient for barrierless reactions
• The dual formalisms of nonextensive thermodynamics for open systems with maximum entropy principle
• The adiabatic static linear response function in nonextensive statistical mechanics
• A nonextensive approach for understanding the van der Waals' equation
• The collision frequencies of charged particles in the complex plasmas with the non-Maxwellian velocity distributions