Noise-induced rectification in out-of-equilibrium structures

Abstract

We consider the motion of overdamped particles over random potentials subjected to a Gaussian white noise and a time-dependent periodic external forcing. The random potential is modeled as the potential resulting from the interaction of a point particle with a random polymer. The random polymer is made up, by means of some stochastic process, from a finite set of possible monomer types. The process is assumed to reach a non-equilibrium stationary state, which means that every realization of a random polymer can be considered as an out-of-equilibrium structure. We show that the net flux of particles over this random medium is non-vanishing when the potential profile on every monomer is symmetric. We prove that this ratchet-like phenomenon is a consequence of the irreversibility of the stochastic process generating the polymer. On the contrary, when the process generating the polymer is at equilibrium (thus fulfilling the detailed balance condition) the system is unable to rectify the motion. We calculate the net flux of the particles in the adiabatic limit for a simple model and we test our theoretical predictions by means of Langevin dynamics simulations. We also show that, out of the adiabatic limit, the system also exhibits current reversals as well as non-monotonic dependence of the diffusion coefficient as a function of forcing amplitude.

Time-irreversibility tests for random-length time series: the matching-time approach applied to DNA

“…which was the formula anticipated in Eqs. ( 21) and (22). Now, once we have an estimation for h, we can obtain an estimation for σ 2 through the expression (A18).…”

“…7 and 8. It is clear that understanding this characteristic might give us a deeper understanding of the physics of DNA, such as protein diffusion along the DNA [20][21][22][23] among other phenomena.…”

Estimating entropy rate from censored symbolic time series: a test for time-irreversibility

“…For instance, in [9] it has been found that real DNA sequences would be spatially irreversible, a characteristic that has been explored aimed to understand the intriguing statistical features of current structure of the genome. The fact that DNA might be spatially irreversible has been used to propose a mechanism of noise-induced rectification of particle motion [10], a mechanism that would be important in the study of biological process involving the DNA transport. Determining the irreversibility of time series has also been the subject of intense research.…”

Non-equilibrium diffusion characteristics of a particle system and the correspondence to a social system

“…Random diffusion is a basic subject for statistical physics and relevant fields, such as the flow in porous media, particle diffusion in turbulent field and so on [1,2,3,4,5,6,7,8]. It is well known that the diffusion is caused by the gradient of macroscopic quantity, density, while it is actualized by the collision among particles at a micro level.…”

“…The calculating results in Refs. [8,14,18] indicate that the diffusion coefficient described by the mean square displacement is of power scaling. The value of the scaling exponent equal to, greater than and less than 1 represents free diffusion, super-diffusion and sub-diffusion, respectively.…”