Interrelations of Different Methods for the Determination of Rates: Flux Over Population, Generalized Reactive Flux, the Lowest Eigenvalue and Its Rayleigh Quotient

The ratio of Kramers' current carrying stationary probability density and the equilibrium probability density is utilized as smoothed characteristic function in the generalized reactive flux method recently proposed by Borkovec and Talkner [J. Chem. Phys. 92, 5307 (1990)]. Under a certain condition on the potential, as generalized transition state rate Kramers' phase space diffusion limited rate is obtained. It then represents an upper bound for the true rate. An approximate expression for the plateau value of the generalized reactive flux yields a Rayleigh quotient for the lowest eigenvalue of the considered Fokker Planck process.