M. van den Broek, C. Van den Broeck
We extend the analysis of a thermal Brownian motor reported in Phys. Rev. Lett. 93, 090601 (2004) by C. Van den Broeck, R. Kawai, and P. Meurs to a three-dimensional configuration. We calculate the friction coefficient, diffusion coefficient, and drift velocity as a function of shape and present estimates based on physically realistic parameter values.
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We have realized a Brownian motor by using cold atoms in a dissipative optical lattice as a model system. In our experiment the optical potential is spatially symmetric and the time-symmetry of the system is broken by applying appropriate zero-mean ac forces. We identify a regime of rectification of forces and a regime of rectification of fluctuations, the latter corresponding to the realization of a Brownian motor.
In this Letter, we show numerically that the rectifying effect of heat flux in a one-dimensional two-segment Frenkel-Kontorova chain demonstrated in recent literature is merely available under the limit of the weak coupling between the two constituent segments. Surprisingly, the rectifying effect will be reversed when the properties of the interface and the system size change. The two types of asymmetric heat conduction are dominated by different mechanisms, which are all induced by the nonlinearity. We further discuss the possibility of the experimental realization of thermal diode or rectifi…
Two losing games, when alternated in a periodic or random fashion, can produce a winning game. This paradox occurs in a family of stochastic processes: if one combines two or more dynamics where a given quantity decreases, the result can be a dynamic system where this quantity increases. The paradox could be applied to a number of stochastic systems and has drawn the attention of researchers from different areas. In this paper we show how the phenomenon can be used to design Brownian or molecular motors, i.e., thermal engines that operate by rectifying fluctuations. We briefly review the liter…
We consider the totally asymmetric exclusion process (TASEP) in one dimension in its maximal current phase. We show, by an exact calculation, that the non-Gaussian part of the fluctuations of density can be described in terms of the statistical properties of a Brownian excursion. Numerical simulations indicate that the description in terms of a Brownian excursion remains valid for more general one dimensional driven systems in their maximal current phase.
In an ensemble of non-interacting Brownian particles, a finite systematic average velocity may temporarily develop, even if it is zero initially. The effect originates from a small nonlinear correction to the dissipative force, causing the equation for the first moment of velocity to couple to moments of higher order. The effect may be relevant when a complex system dissociates in a viscous medium with conservation of momentum.
Two losing gambling games, when alternated in a periodic or random fashion, can produce a winning game. This paradox has been inspired by certain physical systems capable of rectifying fluctuations: the so-called Brownian ratchets. In this paper we review this paradox, from Brownian ratchets to the most recent studies on collective games, providing some intuitive explanations of the unexpected phenomena that we will find along the way.
The efficiency of energy transduction in a temporally asymmetric rocked ratchet is studied. Time asymmetry favours current in one direction and suppresses it in the opposite direction due to which large efficiency ~ 50% is readily obtained. The spatial asymmetry in the potential together with system inhomogeneity may help in further enhancing the efficiency. Fine tuning of system parameters considered leads to multiple current reversals even in the adiabatic regime.
Previous works have shown that time asymmetric forcing on the one hand, as well as non-Gaussian noises on the other, can separately enhance the efficiency and current of a Brownian motor. Here, we study the result of subjecting a Brownian motor to both effects simultaneously. Our results have been compared with those obtained for the Gaussian white noise regime in the adiabatic limit. We find that, although the inclusion of the time asymmetry parameter increases the efficiency value up to a certain extent, for the present case this increase is much less appreciable than in the white noise case…
We investigated three models of Brownian motors which convert rotational diffusion into directed translational motion by switching on and off a potential. In the first model a spatially asymmetric potential generates directed translational motion by rectifying rotational diffusion. It behaves much like a conventional flashing ratchet. The second model utilizes both rotational diffusion and drift to generate translational motion without spatial asymmetry in the potential. This second model can be driven by a combination of a Brownian motor mechanism (diffusion driven) or by powerstroke (drift d…
We study the driven Brownian motion of hard rods in a one-dimensional cosine potential with an amplitude large compared to the thermal energy. In a closed system, we find surprising features of the steady-state current in dependence of the particle density. The form of the current-density relation changes greatly with the particle size and can exhibit both a local maximum and minimum. The changes are caused by an interplay of a barrier reduction, blocking and exchange symmetry effect. The latter leads to a current equal to that of non-interacting particles for a particle size commensurate with…
With this work we investigate an often neglected aspect of Brownian motor transport: The rôle of fluctuations of the noise-induced current and its consequences for the efficiency of rectifying noise. In doing so, we consider a Brownian inertial motor that is driven by an unbiased monochromatic, time-periodic force and thermal noise. Typically, we find that the asymptotic, time- and noise-averaged transport velocities are small, possessing rather broad velocity fluctuations. This implies a corresponding poor performance for the rectification power. However, for tailored profiles of the ratchet …
Based on recent work [L. Machura, M. Kostur, P. Talkner, J. Luczka, and P. Hanggi, Phys. Rev. Lett. 98, 040601 (2007)], we extend the study of inertial Brownian motors to the case of an asymmetric potential. It is found that some transport phenomena appear in the presence of an asymmetric potential. Within tailored parameter regimes, there exists two optimal values of the load at which the mean velocity takes its maximum, which means that a load can facilitate the transport in the two parameter regimes. In addition, the phenomenon of multiple current reversals can be observed when the load is …
Persistence of an active asymmetric rigid Brownian particle in two dimensions
本文研究了二维形状不对称活性布朗粒子的持久概率，解析推导了自由与谐振势阱束缚下推进速度对持久概率的影响，并通过Langevin动力学模拟验证了该方法可区分活性与被动各向异性粒子。
Microscopic model for a Brownian Translator
本文提出布朗平移器微观模型，受布朗陀螺仪启发，通过各向异性温度气体碰撞打破对称性产生漂移，并导出动力学与能量性质的级数表达式，与模拟吻合。
An asymmetric object, undergoing dissipative collisions with surrounding particles, acquires a nonzero average velocity. The latter is calculated analytically by an expansion of the Boltzmann equation and the result is compared with Monte Carlo simulations.
We consider the two dimensional motion of a particle into a confining potential, subjected to Brownian forces, associated with two different temperatures on the orthogonal directions. Exact solutions are obtained for an asymmetric harmonic potential in the overdamped and underdamped regimes, whereas perturbative approaches are used for more general potentials. The resulting non equilibrium stationary state is characterized with a nonzero orthoradial mean current, corresponding to a global rotation of the particle around the center. The rotation is due to two symmetry breaking: two different te…
Individual movements of a rod-like self-propelled particle on a flat substrate are quantified. Biological systems that fit into this description may be the Gram-negative delta-proteobacterium Myxococcus xanthus, Gram-negative bacterium Escherichia coli, and Mitochondria. There are also non-living analogues such as vibrated polar granulates and self-driven anisotropic colloidal particles. For that we study the Brownian motion of an asymmetric rod-like rigid particle self-propelled at a fixed speed along its long axis in two dimensions. The motion of such a particle in a uniform external potenti…
Single-file Brownian motion in periodic structures is an important process in nature and technology, which becomes increasingly amenable for experimental investigation under controlled conditions. To explore and understand generic features of this motion, the Brownian asymmetric simple exclusion process (BASEP) was recently introduced. The BASEP refers to diffusion models, where hard spheres are driven by a constant drag force through a periodic potential. Here, we derive general properties of the rich collective dynamics in the BASEP. Average currents in the steady state change dramatically w…
We propose a stochastic process wherein molecular transport is mediated by asymmetric nucleation of domains on a one-dimensional substrate. Track-driven mechanisms of molecular transport arise in biophysical applications such as Holliday junction positioning and collagenase processivity. In contrast to molecular motors that hydrolyze nucleotide triphosphates and undergo a local molecular conformational change, we show that asymmetric nucleation of hydrolysis waves on a track can also result in directed motion of an attached particle. Asymmetrically cooperative kinetics between ``hydrolyzed'' a…
Dynamics of Brownian particles in asymmetric confinement: Insights into Entropic Stochastic Resonance
该研究探究非对称约束下过阻尼布朗系统的热力学响应，分析周期场频率、噪声强度及横向力对平均做功的影响，揭示约束非对称的降功作用与能熵转变，并提出平均自由飞行时间描述非对称下的熵随机共振。
We show that Brownian motion of a one-dimensional domain wall in a large but finite system yields a $ω^{-3/2}$ power spectrum. This is successfully applied to the totally asymmetric simple exclusion process (TASEP) with open boundaries. An excellent agreement between our theory and numerical results is obtained in a frequency range where the domain wall motion dominates and discreteness of the system is not effective.
We study transport properties of an inertial Brownian particle moving in viscous symmetric periodic structures and driven by an oscillating signal of two harmonic components. We analyze the influence of symmetric, antisymmetric and asymmetric signals on directed transport and reveal the shift symmetry of the stationary averaged velocity of the Brownian particle with respect to the relative phase of two components of the signal. The shift symmetry holds true in all regimes.
We study a continuous-space version of the totally asymmetric simple exclusion process (TASEP), consisting of interacting Brownian particles subject to a driving force in a periodic external potential. Particles are inserted at the leftmost site at rate $α$, hop to the right at unit rate, and are removed at the rightmost site at rate $β$. Our study is motivated by recent experiments on colloidal particles in optical tweezer arrays. The external potential is of the form generated by such an array. Particles spend most of the time near potential minima, approximating the situation in the lattice…
We derive the steady state properties of a general directed ``sandpile'' model in one dimension. Using a central limit theorem for dependent random variables we find the precise conditions for the model to belong to the universality class of the Totally Asymmetric Oslo model, thereby identifying a large universality class of directed sandpiles. We map the avalanche size to the area under a Brownian curve with an absorbing boundary at the origin, motivating us to solve this Brownian curve problem. Thus, we are able to determine the moment generating function for the avalanche-size probability i…
The construction of efficient thermal engines operating at finite times constitutes a fundamental and timely topic in nonequilibrium thermodynamics. We introduce a strategy for optimizing the performance of Brownian engines, based on a collisional approach for unequal interaction times between the system and thermal reservoirs. General (and exact) expressions for thermodynamic properties and their optimized values are obtained, irrespective of the driving forces, asymmetry, the temperatures of reservoirs and protocol to be maximized. Distinct routes for the engine optimization, including maxim…
Mass-based separation of active Brownian particles in an asymmetric channel
本文提出利用非对称通道的空间不对称性、粒子动力学的时间不对称性及外部静态力协同作用，实现不同质量自驱动粒子反向漂移分离，为芯片实验室和粒子分离器件开发提供新机制。
Self-sustained Molecular Rectification without External Driving or Information
本研究展示了一种无需外部能量或信息的分子整流机制，通过离子诱导的界面不对称性实现热波动的定向转化。
Charging capacitors from thermal fluctuations using diodes
本研究提出含结与两个反向二极管的石墨烯波纹耦合电路，利用趋衡过程中的细致平衡暂时破缺，从热浴中为电容器充电且不违背热力学定律。
The Brownian motion of a particle in a one-dimensional periodic potential subjected to a uniform external force F is studied. Using the formula for the diffusion coefficient D obtained by other authors and an alternative one derived from the Fokker-Planck equation in the present work, D is compared with the differential mobility μ= dv/dF where v is the average velocity of the particle. Analytical and numerical calculations indicate that inequality D \ge μk_{B}T, with k_{B} the Boltzmann constant and T the temperature, holds if the periodic potential is symmetric, while it is violated for asymm…
The dynamics of a Brownian particle in a constant magnetic field and time-dependent electric field is studied in the limit of white noise, using a Langevin approach for the classical problem and the path-integral Feynman-Vernon and Caldeira-Leggett framework for the quantum problem. We study the time evolution in configuration space of the probability distribution of an initial pure state represented by an asymmetrical Gaussian wave function and show that it can be described as the superposition of (a) the classical motion of the center of mass, (b) a rotation around the mean position, and (c)…
We discuss two-dimensional diffusion of a Brownian particle confined to a periodic asymmetric channel with soft walls modeled by a parabolic potential. In the channel, the particle experiences different noise intensities, or temperatures, in the transversal and longitudinal directions. The model is inspired by the famous Feynman's ratchet and pawl. Using ideas of the Fick-Jacobs approximation we derive the mean velocity of the particle, the effective diffusion coefficient, and the stationary probability density in the potential unit cell. The derived results are exact for small channel width. …
Brownian motors and Feymann ratchets have been intensively studied in the past decades due to their significance to the foundation of statistical physics. In this work we propose a new type of Brownian motor, i.e., a self-driven motor that only utilizes the temperature difference inside and outside the motor. The motor is a container with asymmetric geometry; when filling of gas, directional motion occurs if its temperature is different from the environment. The essentially new mechanism is that the asymmetric geometry of the container may induce anisotropic thermalization, which results in a …
Persistent random walks are intermediate transport processes between a uniform rectilinear motion and a Brownian motion. They are formed by successive steps of random finite lengths and directions travelled at a fixed speed. The isotropic and symmetric one-dimensional persistent random walk is governed by the telegrapher's equation, also called hyperbolic heat conduction equation. These equations have been designed to resolve the paradox of the infinite speed in the heat and diffusion equations. The finiteness of both the speed and the correlation length leads to several classes of random walk…
Transport of overdamped Brownian particles in a two-dimensional asymmetric tube is investigated in the presence of nonadiabatic periodic driving forces. By using Brownian dynamics simulations we can find that the phenomena in nonadiabatic regime differ from that in adiabatic case. The direction of the current can be reversed by tuning the driving frequency. Remarkably, the current as a function of the driving amplitude exhibits several local maxima at finite driving frequency.
In order to optimize the directed motion of an inertial Brownian motor, we identify the operating conditions that both maximize the motor current and minimize its dispersion. Extensive numerical simulation of an inertial rocked ratchet displays that two quantifiers, namely the energetic efficiency and the Péclet number (or equivalently the Fano factor), suffice to determine the regimes of optimal transport. The effective diffusion of this rocked inertial Brownian motor can be expressed as a generalized fluctuation theorem of the Green -- Kubo type. Addendum and Erratum The expression for the e…
Active Brownian motion commonly assumes spherical overdamped particles. However, self-propelled particles are often neither symmetric nor overdamped yet underlie random fluctuations from their surroundings. Active Brownian motion has already been generalized to include asymmetric particles. Separately, recent findings have shown the importance of inertial effects for particles of macroscopic size or in low-friction environments. We aim to consolidate the previous findings into the general description of a self-propelled asymmetric particle with inertia. We derive the Langevin equation of such …
Asymmetry-controlled resonant transport in a Brownian flashing ratchet
该研究针对带分段线性不对称周期势的一维布朗闪烁棘轮，通过数值模拟揭示其稳态电流对切换频率的非单调依赖关系，明确了共振频率的标度规律并给出物理解释。
Relativistic Brownian motion can be inexpensively demonstrated on a graphene chip. The interplay of stochastic and relativistic dynamics, governing the transport of charge carrier in graphene, induces noise-controlled effects such as (i) a stochastic effective mass, detectable as a suppression of the particle mobility with increasing the temperature; (ii) a transverse ratchet effect, measurable as a net current orthogonal to an ac drive on an asymmetric substrate, and (iii) a chaotic stochastic resonance. Such properties can be of practical applications in the emerging graphene technology.
The flashing Brownian ratchet is a stochastic process that alternates between two regimes, a one-dimensional Brownian motion and a Brownian ratchet, the latter being a one-dimensional diffusion process that drifts towards a minimum of a periodic asymmetric sawtooth potential. The result is directed motion. In the presence of a static homogeneous force that acts in the direction opposite that of the directed motion, there is a reduction (or even a reversal) of the directed motion effect. Such a process may be called a tilted flashing Brownian ratchet. We show how one can study this process nume…
An engine producing a finite power at the ideal (Carnot) efficiency is a dream engine, which is not prohibited by the thermodynamic second law. Some years ago, a two-terminal heat engine with {\em asymmetric} Onsager coefficients in the linear response regime was suggested by Benenti, Saito, and Casati [Phys. Rev. Lett. {\bf 106}, 230602 (2011)], as a prototypical system to make such a dream come true with non-divergent system parameter values. However, such a system has never been realized in spite of many trials. Here, we introduce an exactly solvable two-terminal Brownian heat engine with t…
Energy-Efficient Pseudo-Ratchet for Brownian Computers through One-Dimensional Quantum Brownian Motion
本文提出基于一维量子布朗运动的伪棘轮机制，利用量子共振效应实现无外部力驱动的单向传输，为布朗计算机提供低能耗计算方案。
We consider the one-dimensional Kardar-Parisi-Zhang (KPZ) equation with half Brownian motion initial condition, studied previously through the weakly asymmetric simple exclusion process. We employ the replica Bethe ansatz and show that the generating function of the exponential moments of the height is expressed as a Fredholm determinant. From this the height distribution and its asymptotics are studied. Furthermore using the replica method we also discuss the multi-point height distribution. We find that some nice properties of the deformed Airy functions play an important role in the analysi…
The motion of a Brownian particle in the presence of Coulomb friction and an asymmetric spatial potential was evaluated in this study. The system exhibits a ratchet effect, i.e., an average directed motion even in the absence of an external force, induced by the coupling of non-equilibrium conditions with the spatial asymmetry. Both the average motion and the fluctuations of the Brownian particle were analysed. The stationary velocity shows a non-monotonic behaviour as a function of both the temperature and the viscosity of the bath. The diffusion properties of the particle, which show several…
In this work we experimentally study the behavior of a freely-rotating asymmetric probe immersed in a vibrated granular medium. For a wide variety of vibration conditions the probe exhibits a steady rotation whose direction is constant with respect to the asymmetry. By changing the vibration amplitude and by filtering the noise in different frequency bands we show that the velocity of rotation does not depend only on the RMS acceleration $Γ$, but also on the amount of energy provided to two separate frequency bands which are revealed to be important for the dynamics of the granular medium: the…
A reversal of the particle current in rocking Brownian motors was predicted more than 20 years ago; however, an experimental verification and a deeper insight into the underlying mechanisms remained elusive. Here, we investigate the high frequency behaviour of a rocking Brownian motor for charged nanoparticles based on electrostatic interactions in a 3D shaped nanofluidic slit and electro-osmotic forcing of the particles. A sub ms temporal and $\approx\,10\,$nm spatial resolution of the 60 nm gold spheres allows us to measure the time-resolved and frequency dependent evolution of the particle …
Diffusion and rectification of Brownian particles powered by a rotating wheel are numerically investigated in a two-dimensional channel. The nonequilibrium driving comes from the rotating wheel, which can break thermodynamical equilibrium and induce the directed transport in an asymmetric potential. It is found that the direction of the transport along the potential is determined by the asymmetry of the potential and the position of the wheel. The average velocity is a peaked function of the angular speed (or the diffusion coefficient) and the position of the peak shifts to large angular speed…
We study the mean velocity and diffusion constant in three related models of molecular Brownian ratchets. Brownian ratchets can be used to describe translocation of biopolymers like DNA through nanopores in cells in the presence of chaperones on the trans side of the pore. Chaperones can bind to the polymer and prevent it from sliding back through the pore. First, we study a simple model that describes the translocation in terms of an asymmetric random walk. It serves as an introductory example but already captures the main features of a Brownian ratchet. We then provide an analytical expressi…
We show that the recent experimental observation of the rectification of swimming bacteria in a system with an array of asymmetric barriers occurs due to the ballistic component of the bacteria trajectories introduced by the bacterial "motor." Each bacteria selects a random direction for motion and then moves in this direction for a fixed period of time before randomly changing its orientation and moving in a new direction. In the limit where the bacteria undergo only Brownian motion, rectification by the barriers does not occur. We also examine the effects of steric interactions between the b…
We consider a massive inelastic piston, whose opposite faces have different coefficients of restitution, moving under the action of an infinitely dilute gas of hard disks maintained at a fixed temperature. The dynamics of the piston is Markovian and obeys a continuous Master Equation: however, the asymmetry of restitution coefficients induces a violation of detailed balance and a net drift of the piston, as in a Brownian ratchet. Numerical investigations of such non-equilibrium stationary state show that the velocity fluctuations of the piston are symmetric around the mean value only in the li…
Einstein realised that the fluctuations of a Brownian particle can be used to ascertain properties of its environment. A large number of experiments have since exploited the Brownian motion of colloidal particles for studies of dissipative processes, providing insight into soft matter physics, and leading to applications from energy harvesting to medical imaging. Here we use optically levitated nanospheres that are heated to investigate the non-equilibrium properties of the gas surrounding them. Analysing the sphere's Brownian motion allows us to determine the temperature of the centre-of-mass…
Local Time Statistics and Permeable Barrier Crossing: from Poisson to Birth-Death Diffusion Equations
本文建立布朗运动穿越可渗透屏障的微观模型，推导穿越次数分布与渗透率统计定义，求解生灭扩散方程，并证明不对称屏障可诱导噪声漂移及非平衡稳态。
The Gravitational Aspect of Information: The Physical Reality of Asymmetric "Distance"
该研究通过展示布朗桥在规范条件下的时间演化与高斯分布流形上的m-测地线一致，揭示了信息不对称距离在物理中的根本作用，并推动了信息等价原理的发展。
The rectification of unbiased fluctuations, also known as the ratchet effect, is normally obtained under statistical non-equilibrium conditions. Here we propose a new ratchet mechanism where a thermal bath solicits the random rotation of an asymmetric wheel, which is also subject to Coulomb friction due to solid-on-solid contacts. Numerical simulations and analytical calculations demonstrate a net drift induced by friction. If the thermal bath is replaced by a granular gas, the well known granular ratchet effect also intervenes, becoming dominant at high collision rates. For our chosen wheel s…
Two headed motor proteins, such as kinesin and dynein, hidrolyze environmental ATP in order to propel unidirectionally along cytoskeletal filaments such as microtubules. In the case of kinesin, protein heads bind primarily on the alpha tubulin site of asymmetric alpha-beta 8nm-long tubulin dimers that constitute the microtubular protofilaments. Kinesin dimers overcome local binding forces up to 5pN and are known to move on protofilaments with ATP concentration-dependent speeds while hydrolizing on average one ATP molecule per 8nm step. The salient features of protein trajectories are the disti…
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