Klimontovich's contributions to the kinetic theory of nonlinear Brownian motion and new developments (original) (raw)

Stochastic thermodynamics of active Brownian particles

Physical Review E, 2013

Examples of self propulsion in strongly fluctuating environment is abound in nature, e.g., molecular motors and pumps operating in living cells. Starting from Langevin equation of motion, we develop a stochastic thermodynamic description of non-interacting self propelled particles using simple models of velocity dependent forces. We derive fluctuation theorems for entropy production and a modified fluctuation dissipation relation, characterizing the linear response at non-equilibrium steady states. We study these notions in a simple model of molecular motors, and in the Rayleigh-Helmholtz and energy-depot model of self propelled particles.

Dynamics of Active Brownian Particles in Plasma

Molecules, 2021

Experimental data on the active Brownian motion of single particles in the RF (radio-frequency) discharge plasma under the influence of thermophoretic force, induced by laser radiation, depending on the material and type of surface of the particle, are presented. Unlike passive Brownian particles, active Brownian particles, also known as micro-swimmers, move directionally. It was shown that different dust particles in gas discharge plasma can convert the energy of a surrounding medium (laser radiation) into the kinetic energy of motion. The movement of the active particle is a superposition of chaotic motion and self-propulsion.

Brownian particles far from equilibrium

European Physical Journal B, 2000

We study a model of Brownian particles which are pumped with energy by means of a non-linear friction function, for which different types are discussed. A suitable expression for a non-linear, velocity-dependent friction function is derived by considering an internal energy depot of the Brownian particles. In this case, the friction function describes the pumping of energy in the range of small velocities, while in the range of large velocities the known limit of dissipative friction is reached. In order to investigate the influence of additional energy supply, we discuss the velocity distribution function for different cases. Analytical solutions of the corresponding Fokker-Planck equation in 2d are presented and compared with computer simulations. Different to the case of passive Brownian motion, we find several new features of the dynamics, such as the formation of limit cycles in the four-dimensional phase-space, a large mean squared displacement which increases quadratically with the energy supply, or non-equilibrium velocity distributions with crater-like form. Further, we point to some generalizations and possible applications of the model.

Towards a unified dynamical theory of the Brownian particle in an ideal gas

Communications in Mathematical Physics, 1987

We consider the trajectory Q M (t) of a Brownian particle of mass Min an ideal gas of identical particles of mass 1 and of density 1 in equilibrium at inverse temperature 1 (the dynamics is uniform motion plus elastic collisions with the Brownian particle). Our theory, in dimension one, describes a variety of limiting processes -containing the Wiener process and the Ornstein-Uhlenbeck process -for A ~1 /2 Q M(A \At) depending on the asymptotic behaviour of M(A). Part of the theory is hypothetical while another part relies upon known results. We also prove that, if A* +ε <ζM(A)<ζA, then A' lβ Q M(A \Af) converges to a Wiener process whose variance is known from papers of Sinai-Soloveichik and of the present authors.

Microscopic theory of brownian motion

Physica A: Statistical Mechanics and its Applications, 1975

In this article nonlinear Langevin equations for a brownian (B) particle are derived and analyzed. Attention is focussed on the role of nonlinear B particle momentum (P) modes (powers of P). The multimode Mori formalism is used to derive equations of motion for P(t) for different numbers n of modes included in the description. The well-known linear equation of Mori corresponds to the case n = 1. Friction kernels and random forces in these equations exhibit slow decay and mass ratio (2) expansion anomalies due to mode coupling. The nonlinear Langevin equation obtained for a complete mode set (n = co) is free of these difficulties and is used to examine the first correction [0(24)] to standard 0(22) results. Although no closed set of nonlinear Langewin equations exists at order ;t*, a truncated set extends standard momentum correlation function predictions. * In the present notation, the one mode quantities of sec.2 are Km(e)-= K~l(e) and A~l(e) Axxx(e).

Brownian particle in non-equilibrium plasma

Condensed Matter Physics, 2009

The stationary distribution function of Brownian particles in a nonequilibrium dusty plasma is calculated with regard to electron and ion absorption by grains. The distribution is shown to be considerably different from the distribution function of ordinary Brownian particles in thermal equilibrium. A criterion for the grain-structure formation in a nonequilibrium dusty plasma is derived.

Collective effects in confined active Brownian particles

The Journal of Chemical Physics, 2021

We investigate a two-dimensional system of active particles confined to a narrow annular domain. Despite the absence of explicit interactions among the velocities or the active forces of different particles, the system displays a transition from a disordered and stuck state to an ordered state of global collective motion where the particles rotate persistently clockwise or anticlockwise. We describe this behavior by introducing a suitable order parameter, the velocity polarization, measuring the global alignment of the particles' velocities along the tangential direction of the ring. We also measure the spatial velocity correlation function and its correlation length to characterize the two states. In the rotating phase, the velocity correlation displays an algebraic decay that is analytically predicted together with its correlation length while in the stuck regime the velocity correlation decays exponentially with a correlation length that increases with the persistence time. In the first case, the correlation (and, in particular, its correlation length) does not depend on the active force but the system size only. The global collective motion, an effect caused by the interplay between finite-size, periodicity, and persistent active forces, disappears as the size of the ring becomes infinite, suggesting that this phenomenon does not correspond to a phase transition in the usual thermodynamic sense.

Active Brownian particles: Entropy production and fluctuation response

Physical Review E, 2014

Within the Rayleigh-Helmholtz model of active Brownian particles activity is due to a non-linear velocity dependent force. In the presence of external trapping potential or constant force, the steady state of the system breaks detailed balance producing a net entropy. Using molecular dynamics simulations, we obtain the probability distributions of entropy production in these steady states. The distribution functions obey fluctuation theorems for entropy production. Using the simulation, we further show that the steady state response function obeys a modified fluctuation-dissipation relation.

Brownian motion of charged particles driven by correlated noise

arXiv (Cornell University), 2011

Stochastic motion of charged particles in the magnetic field was first studied almost half a century ago in the classical works by Taylor and Kurşunoğlu in connection with the diffusion of electrons and ions in plasma. In their works the long-time limits of the mean square displacement (MSD) of the particles have been found. Later Furuse on the basis of standard Langevin theory generalized their results for arbitrary times. The currently observed revival of these problems is mainly related to memory effects in the diffusion of particles, which appear when colored random forces act on the particles from their surroundings. In the present work an exact analytical solution of the generalized Langevin equation has been found for the motion of the particle in an external magnetic field when the random force is exponentially correlated in the time. The obtained MSD of the particle motion across the field contains a term proportional to the time, a constant term, and contributions exponentially decaying in the time. The results are more general than the previous results from the literature and are obtained in a considerably simpler way applicable to many other problems of the Brownian motion with memory.

Charged Brownian particles: Kramers and Smoluchowski equations and the hydrothermodynamical picture

Physica A: Statistical Mechanics and its Applications, 2011

We consider a charged Brownian gas under the influence of external and non uniform electric, magnetic and mechanical fields, immersed in a non uniform bath temperature. With the collision time as an expansion parameter, we study the solution to the associated Kramers equation, including a linear reactive term. To first order we obtain the asymptotic (overdamped) regime, governed by transport equations, namely: for the particle's density, a Smoluchowskireactive like equation; for the particle's momentum density, a generalized Ohm's like equation; and for the particleś energy density, a Maxwell-Cattaneo like equation. Defining a nonequilibrium temperature as the mean kinetic energy density, and introducing Boltzmann's entropy density via the one particle distribution function, we present a complete thermohydrodynamical picture for a charged Brownian gas. We probe the validity of the local equilibrium approximation, Onsager relations, variational principles associated to the entropy production, and apply our results to: carrier transport in semiconductors, hot carriers and Brownian motors. Finally, we outline a method to incorporate non linear reactive kinetics and a mean field approach to interacting Brownian particles.