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We study a classical two-state stochastic system in a sea of substrates andproducts (absorbing states), which can be interpreted as a singleMichaelis-Menten catalyzing enzyme or as a channel on a cell surface. Weintroduce a novel general method and use it to derive the expression for thefull counting statistics of transitions among the absorbing states. For theevolution of the system under a periodic perturbation of the kinetic rates, thelatter contains a term with a purely geometrical (the Berry phase)interpretation. This term gives rise to a pump current between the absorbingstates, which is due entirely to the stochastic nature of the system. Wecalculate the first two cumulants of this current, and we argue that it isobservable experimentally

On the momentum transfer dependence of the atomic motions in the α-relaxation range. Polymers vs. low–molecular-weight glass-forming systems