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Forced thermal ratchets.

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TLDR
In this paper, the authors considered a Brownian particle in a periodic potential under heavy damping and showed that if the particle is subject to an external force having time correlations, detailed balance is lost and the particle can exhibit a nonzero net drift speed.
Abstract
We consider a Brownian particle in a periodic potential under heavy damping. The second law forbids it from displaying any net drift speed, even if the symmetry of the potential is broken. But if the particle is subject to an external force having time correlations, detailed balance is lost and the particle can exhibit a nonzero net drift speed. Thus, broken symmetry and time correlations are sufficient ingredients for transport.

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Citations
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Nonlinear dynamics of spatio-temporally driven lattices

TL;DR: In this paper, the classical and quantum dynamics of particles in spatiotemporally driven lattices are studied, where a locally varying time-dependent driving leads to novel phenomena yielding an increased control over the non-equilibrium dynamics of the propagating particles compared to the case of a uniformly driven lattice.
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Effect of Asymmetry of Dichotomous Noise on Transport of Particles

TL;DR: In this paper, the effect of the asymmetry of the additive and multiplicative dichotomous noises on the transport of the particles, in the presence of spatial symmetry and asymmetry, respectively, was investigated.
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Collective transient ratchet transport induced by many elastically interacting particles.

TL;DR: In this paper, the authors demonstrate that coupled ratchets exhibit collective transient ratchet transport and demonstrate that physical devices built with coupled ratchet systems should present large collective transient transport of particles, whose technological applications are undoubtedly appealing and feasible.
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Inter-particle ratchet effect determines global current of heterogeneous particles diffusing in confinement

TL;DR: In this article, the authors consider a model of $N$ volume-excluding spheres in a $d$-dimensional tube, and derive the exact joint gap distribution for driven tracers in a passive bath.
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Charged Particle Motion in Temporal Chaotic and Spatiotemporal Chaotic Fields

TL;DR: In this paper, the authors investigated particle motion in spatiotemporal chaotic and temporal chaotic fields and found that the particle drifts relative to the steady wave, in contrast to that in the temporal chaotic field where the particle motion is localized in a trough of the wave field.
References
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Book

Stochastic processes in physics and chemistry

TL;DR: In this article, the authors introduce the Fokker-planck equation, the Langevin approach, and the diffusion type of the master equation, as well as the statistics of jump events.

Stochastic Processes in Physics and Chemistry

Abstract: Preface to the first edition. Preface to the second edition. Abbreviated references. I. Stochastic variables. II. Random events. III. Stochastic processes. IV. Markov processes. V. The master equation. VI. One-step processes. VII. Chemical reactions. VIII. The Fokker-Planck equation. IX. The Langevin approach. X. The expansion of the master equation. XI. The diffusion type. XII. First-passage problems. XIII. Unstable systems. XIV. Fluctuations in continuous systems. XV. The statistics of jump events. XVI. Stochastic differential equations. XVII. Stochastic behavior of quantum systems.
Book

Molecular Cell Biology

TL;DR: Molecular cell biology, Molecular cell biology , مرکز فناوری اطلاعات و اصاع رسانی, کδاوρزی
Book

The Fokker-Planck Equation: Methods of Solution and Applications

Hannes Risken
TL;DR: In this paper, the Fokker-Planck Equation for N Variables (FPE) was extended to N = 1 variable and N = 2 variables, where N is the number of variables in the system.