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

TL;DR

This paper extends transition state theory to nonequilibrium systems characterized by power-law distributions, providing generalized rate constants and Arrhenius equations for such systems modeled by Langevin and Fokker-Planck equations.

Contribution

It introduces a novel generalization of TST applicable to nonequilibrium systems with power-law distributions, derived from stochastic dynamics.

Findings

Generalized TST rate constants for 1D and nD systems

Derivation of a generalized Arrhenius rate for power-law distributions

Applicable to systems far from thermal equilibrium

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.