Decay of unstable equilibrium and nonequilibrium states with inverse probability current taken into account

We study the causes of noise delayed decay of unstable states in nonlinear dynamic systems within the framework of the overdamped Brownian motion model. For the analysis, we use the exact expressions for the decay times of unstable states, which take into account the inverse probability current in contrast to the well-known mean first passage time method. These expressions are valid for any intensity of fluctuations and for arbitrary potential profiles. The effect of delay is shown to arise under the decay of unstable nonequilibrium states due to the action of two different mechanisms. These mechanisms are caused by the inverse probability current and by the nonlinearity of potential describing an unstable state.