15 research outputs found
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
Particle current in symmetric exclusion process with time-dependent hopping rates
In a recent study, (Jain et al 2007 Phys. Rev. Lett. 99 190601), a symmetric
exclusion process with time-dependent hopping rates was introduced. Using
simulations and a perturbation theory, it was shown that if the hopping rates
at two neighboring sites of a closed ring vary periodically in time and have a
relative phase difference, there is a net DC current which decreases inversely
with the system size. In this work, we simplify and generalize our earlier
treatment. We study a model where hopping rates at all sites vary periodically
in time, and show that for certain choices of relative phases, a DC current of
order unity can be obtained. Our results are obtained using a perturbation
theory in the amplitude of the time-dependent part of the hopping rate. We also
present results obtained in a sudden approximation that assumes large
modulation frequency.Comment: 17 pages, 2 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
Generally covariant state-dependent diffusion
Statistical invariance of Wiener increments under SO(n) rotations provides a
notion of gauge transformation of state-dependent Brownian motion. We show that
the stochastic dynamics of non gauge-invariant systems is not unambiguously
defined. They typically do not relax to equilibrium steady states even in the
absence of extenal forces. Assuming both coordinate covariance and gauge
invariance, we derive a second-order Langevin equation with state-dependent
diffusion matrix and vanishing environmental forces. It differs from previous
proposals but nevertheless entails the Einstein relation, a Maxwellian
conditional steady state for the velocities, and the equipartition theorem. The
over-damping limit leads to a stochastic differential equation in state space
that cannot be interpreted as a pure differential (Ito, Stratonovich or else).
At odds with the latter interpretations, the corresponding Fokker-Planck
equation admits an equilibrium steady state; a detailed comparison with other
theories of state-dependent diffusion is carried out. We propose this as a
theory of diffusion in a heat bath with varying temperature. Besides
equilibrium, a crucial experimental signature is the non-uniform steady spatial
distribution.Comment: 24 page