The thermal activation over a potential barrier in a stochastically modified system is analyzed. If colored noise perturbs the potential one can observe the famous resonant activation phenomenon. We compare this effect with the results caused by correlated fluctuations of the temperature. For high potential barrier stochastic variations of temperature lead to resonant activation as well. However, for low-barrier or barrierless evolution this effect disappears. We formulate an analytical condition separating these cases and present a physical interpretation of both types of behavior.

We revise the problem of thermally activated crossing of a fluctuating potential barrier, laying stress on the asymmetry of the barrier. Considering as a working model a paradigmatic triangular dichotomously varying potential landscape we find an atypical dependence of the mean first-passage time on the correlation time tau of fluctuations. Namely, in the range of small tau an additional maximum appears. We propose a qualitative explanation of this feature emphasizing the relevance of dynamics in the vicinity of the barrier top, i.e., recrossing, which generally has not been recognized by this time in this particular context. Moreover, we observe that addition of fast barrier fluctuations of some finite intensity needs not to increase the relaxation rate, as has been indicated many times in extensive studies related to the resonant activation phenomenon. Our findings are confirmed numerically for some other systems.

Ionic channels form pores in biomembranes. These pores are large macromolecular structures. Due to thermal fluctuations of countless degrees-offreedom of the biomembrane material, the actual form of the pores is permanently subject to modification. Furthermore, the arrival of an ion at the binding site can change this form by repolarizing the surrounding aminoacids. In any case the variations of the pore structure are stochastic. In this paper, we discuss the effect of such modifications on the channel conductivity. Applying a simple kinetic description, we show that stochastic variations in channel properties can significantly alter the ionic current, even leading to its substantial increase or decrease for the specific matching of some time-scales of the system.