Robust quantization of a molecular motor motion in a stochastic environment

We explore quantization of the response of a molecular motor to periodic modulation of control parameters. We formulate the Pumping-Quantization Theorem (PQT) that identifies the conditions for robust integer quantized behavior of a periodically driven molecular machine. Implication of PQT on experiments with catenane molecules are discussed.Comment: 7 pages, 4 figures. J. Chem. Phys. Communications (in press

Duality and fluctuation relations for statistics of currents on cyclic graphs

We consider stochastic motion of a particle on a cyclic graph with arbitrarily periodic time dependent kinetic rates. We demonstrate duality relations for statistics of currents in this model and in its continuous version of a diffusion in one dimension. Our duality relations are valid beyond detailed balance constraints and lead to exact expressions that relate statistics of currents induced by dual driving protocols. We also show that previously known no-pumping theorems and some of the fluctuation relations, when they are applied to cyclic graphs or to one dimensional diffusion, are special consequences of our duality.Comment: 2 figure, 6 pages (In twocolumn). Accepted by JSTA

Pumping-Restriction Theorem for Stochastic Networks

We formulate an exact result, which we refer to as the pumping restriction theorem (PRT). It imposes strong restrictions on the currents generated by periodic driving in a generic dissipative system with detailed balance. Our theorem unifies previously known results with the new ones and provides a universal nonperturbative approach to explore further restrictions on the stochastic pump effect in non-adiabatically driven systems.Comment: 4 pages, 5 figure

Geometric Universality of Currents

We discuss a non-equilibrium statistical system on a graph or network. Identical particles are injected, interact with each other, traverse, and leave the graph in a stochastic manner described in terms of Poisson rates, possibly dependent on time and instantaneous occupation numbers at the nodes of the graph. We show that under the assumption of constancy of the relative rates, the system demonstrates a profound statistical symmetry, resulting in geometric universality of the statistics of the particle currents. This phenomenon applies broadly to many man-made and natural open stochastic systems, such as queuing of packages over the internet, transport of electrons and quasi-particles in mesoscopic systems, and chains of reactions in bio-chemical networks. We illustrate the utility of our general approach using two enabling examples from the two latter disciplines.Comment: 15 pages, 5 figure