Nonequilibrium Fluctuations of a Brownian Particle in a Medium with Production of Entropy

2021 ◽  
pp. 47-56
Author(s):  
A.N. Morozov
Keyword(s):  
Brownian Motion ◽  
Particle Velocity ◽  
Brownian Particle ◽  
Characteristic Functions ◽  
Equilibrium Fluctuations ◽  
Nonequilibrium Fluctuations ◽  
Logarithmic Law ◽  
Production Of Entropy ◽  
Logarithmic Dependence ◽  
Research Show

The study statistically describes Brownian motion in a locally nonequilibrium medium, taking into account the production of entropy, and proposes to describe the nonequilibrium fluctuations of the velocity of a Brownian particle using a linear integro-differential equation. The characteristic functions of fluctuations of the Brownian particle velocity are obtained, which make it possible to carry out a complete statistical description of Brownian motion in a medium with the production of entropy. Findings of research show that the variance of these fluctuations increases with time according to the logarithmic law. The correlation function of fluctuations of the Brownian particle velocity is calculated and it is shown that it consists of two terms. The first term, which has a power-law dependence, describes equilibrium fluctuations, and the second, which has a logarithmic dependence, describes nonequilibrium fluctuations

A perfect probe: Resonance of underdamped scaled Brownian motion

2021 ◽  
Author(s):  
Yuhui Luo ◽  
Chunhua Zeng ◽  
Baowen Li
Keyword(s):  
Brownian Motion ◽  
Single Particle ◽  
Brownian Particle ◽  
Bistable System ◽  
Velocity Autocorrelation Function ◽  
Interacting Particles ◽  
Velocity Autocorrelation ◽  
Spectrum Density ◽  
Coupling Strengths ◽  
And Diffusion

Abstract We numerically investigate the resonance of the underdamped scaled Brownian motion in a bistable system for both cases of a single particle and interacting particles. Through the velocity autocorrelation function (VACF) and mean squared displacement (MSD) of a single particle, we find that for the steady state, diffusions are ballistic at short times and then become normal for most of parameter regimes. However, for certain parameter regimes, both VACF and MSD suggest that the transition between superdiffusion and subdiffusion takes place at intermediate times, and diffusion becomes normal at long times. Via the power spectrum density corresponding to the transitions, we find that there exists a nontrivial resonance. For interacting particles, we find that the interaction between the probe particle and other particles can lead to the resonance, too. Thus we theoretically propose the system with the Brownian particle as a probe, which can detect the temperature of the system and identify the number of the particles or the types of different coupling strengths in the system. The probe is potentially useful for detecting microscopic and nanometer-scale particles and for identifying cancer cells or healthy ones.

scholarly journals A four-dimensional random motion at finite speed

2006 ◽  
Vol 43 (4) ◽  
pp. 1107-1118 ◽  
Author(s):  
Alexander D. Kolesnik
Keyword(s):  
Brownian Motion ◽  
Poisson Process ◽  
Transition Density ◽  
Random Motion ◽  
Characteristic Functions ◽  
Conditional Distributions ◽  
Continuous Component ◽  
Absolutely Continuous ◽  
Finite Speed ◽  
Uniform Law

We consider the random motion of a particle that moves with constant finite speed in the space ℝ4 and, at Poisson-distributed times, changes its direction with uniform law on the unit four-sphere. For the particle's position, X(t) = (X1(t), X2(t), X3(t), X4(t)), t > 0, we obtain the explicit forms of the conditional characteristic functions and conditional distributions when the number of changes of directions is fixed. From this we derive the explicit probability law, f(x, t), x ∈ ℝ4, t ≥ 0, of X(t). We also show that, under the Kac condition on the speed of the motion and the intensity of the switching Poisson process, the density, p(x,t), of the absolutely continuous component of f(x,t) tends to the transition density of the four-dimensional Brownian motion with zero drift and infinitesimal variance σ2 = ½.

scholarly journals Thermal Fluctuations in Electric Circuits and the Brownian Motion

2010 ◽  
Vol 61 (4) ◽  
pp. 252-256 ◽  
Author(s):  
Gabriela Vasziová ◽  
Jana Tóthová ◽  
Lukáš Glod ◽  
Vladimír Lisý
Keyword(s):  
Brownian Motion ◽  
Brownian Particle ◽  
Mean Square Displacement ◽  
Thermal Fluctuations ◽  
Stochastic Equations ◽  
Thermal Bath ◽  
Current Fluctuations ◽  
Electric Circuits ◽  
The Mean ◽  
Optically Trapped

Thermal Fluctuations in Electric Circuits and the Brownian MotionIn this work we explore the mathematical correspondence between the Langevin equation that describes the motion of a Brownian particle (BP) and the equations for the time evolution of the charge in electric circuits, which are in contact with the thermal bath. The mean quadrate of the fluctuating electric charge in simple circuits and the mean square displacement of the optically trapped BP are governed by the same equations. We solve these equations using an efficient approach that allows us converting the stochastic equations to ordinary differential equations. From the obtained solutions the autocorrelation function of the current and the spectral density of the current fluctuations are found. As distinct from previous works, the inertial and memory effects are taken into account.

BROWNIAN MOTION WITH ADHESION: LINEAR AND QUADRATIC NOISE

2012 ◽  
Vol 11 (03) ◽  
pp. 1242001
Author(s):  
M. GITTERMAN
Keyword(s):  
Brownian Motion ◽  
Stationary State ◽  
Large Amplitude ◽  
Brownian Particle ◽  
Periodic Field ◽  
Second Moment ◽  
New Type ◽  
Quadratic Noise

We consider a new type of the Brownian motion, in which the surrounding molecules are capable not only of colliding with the Brownian particle, but also of adhering to the Brownian particle for some time, thereby randomly changing its mass. The second moment, 〈v2〉, becomes negative either due to the large strength of the mass fluctuations or due to the large amplitude of an external periodic field indicating an instability of the system, which cannot reach the stationary state.

Brownian Motion of Rotating Particles

1968 ◽  
Vol 23 (4) ◽  
pp. 597-609 ◽  
Author(s):  
Siegfried Hess
Keyword(s):  
Brownian Motion ◽  
Angular Velocity ◽  
Brownian Particle ◽  
Planck Equation ◽  
Transverse Force ◽  
Particle Collision ◽  
Fokker Planck Equation ◽  
Rotational Motions ◽  
Transport Relaxation ◽  
Fokker Planck

A kinetic theory for the Brownian motion of spherical rotating particles is given starting from a generalized Fokker-Planck equation. The generalized Fokker-Planck collision operator is a sum of two ordinary Fokker-Planck differential operators in velocity and angular velocity space respectively plus a third term which provides a coupling of translational and rotational motions. This term stems from a transverse force proportional to the cross product of velocity and angular velocity of a Brownian particle. Collision brackets pertaining to the generalized Fokker-Planck operator are defined and their general properties are discussed. Application of WALDMANN'S moment method to the Fokker-Planck equation yields a set of coupled linear differential equations (transport-relaxation equations) for certain local mean values. The constitutive laws for diffusion, heat conduction by Brownian particles and spin diffusion are deduced from the transport-relaxation equations. The transport-relaxations coefficients appearing in them are given in terms of the two friction coefficients for the damping of translational and rotational motions and a third coefficient which is a measure of the transverse force. By the coupling of translational and rotational motions a diffusion flow gives rise to a correlation of linear and angular velocities.

Brownian Motion as an Irreversible Non-Markovian Process

2019 ◽  
pp. 94-103
Author(s):  
A.N. Morozov
Keyword(s):  
Brownian Motion ◽  
Small Volume ◽  
Flicker Noise ◽  
Brownian Particle ◽  
Low Frequency ◽  
Frequency Region ◽  
Markovian Process ◽  
Irreversible Processes ◽  
Velocity Fluctuations ◽  
Non Equilibrium

The paper presents a method of describing Brownian motion in a non-equilibrium medium for the case of irreversible processes. We computed spectral density of velocity fluctuations for a Brownian particle in a non-equilibrium medium and determined that in the low-frequency region it is represented by flicker noise. We employed the method we developed to describe Brownian motion in a non-equilibrium medium to compute fluctuations of current in a small volume of an electrolyte. We derived estimations of the Hooge parameter magnitude and the randomisation time constant for ions in an electrolyte, which match the estimations obtained via experiments

Thermal Conductivity Equations Based on Brownian Motion in Suspensions of Nanoparticles (Nanofluids)

2008 ◽  
Vol 130 (4) ◽  
Author(s):  
Bao Yang
Keyword(s):  
Experimental Data ◽  
Thermal Conductivity ◽  
Brownian Motion ◽  
Relaxation Time ◽  
Kinetic Theory ◽  
Significant Role ◽  
Particle Velocity ◽  
Long Time ◽  
Theoretical Results ◽  
Enhanced Thermal Conductivity

Thermal conductivity equations for the suspension of nanoparticles (nanofluids) have been derived from the kinetic theory of particles under relaxation time approximations. These equations, which take into account the microconvection caused by the particle Brownian motion, can be used to evaluate the contribution of particle Brownian motion to thermal transport in nanofluids. The relaxation time of the particle Brownian motion is found to be significantly affected by the long-time tail in Brownian motion, which indicates a surprising persistence of particle velocity. The long-time tail in Brownian motion could play a significant role in the enhanced thermal conductivity in nanofluids, as suggested by the comparison between the theoretical results and the experimental data for the Al2O3-in-water nanofluids.

THE NONZERO MINIMUM OF THE DIFFUSION PARAMETER AND THE UNCERTAINTY PRINCIPLE FOR A BROWNIAN PARTICLE

2002 ◽  
Vol 16 (13) ◽  
pp. 467-471 ◽  
Author(s):  
E. MAMONTOV ◽  
M. WILLANDER
Keyword(s):  
Stochastic Process ◽  
Brownian Motion ◽  
Differential Equations ◽  
Uncertainty Principle ◽  
Brownian Particle ◽  
Diffusion Parameter ◽  
Quantum Mechanical ◽  
Mathematical Form ◽  
Quantitative Results ◽  
Heisenberg's Uncertainty Principle

The limits of applicability of many classical (non-quantum-mechanical) theories are not sharp. These theories are sometimes applied to the problems which are, in their nature, not very well suited for that. Two of the most widely used classical approaches are the theory of diffusion stochastic process and Itô's stochastic differential equations. It includes the Brownian-motion treatment as the basic particular case. The present work shows that, for quantum-mechanical reasons, the diffusion parameter of a Brownian particle cannot be arbitrarily small since it has a nonzero minimum value. This fact leads to the version of Heisenberg's uncertainty principle for a Brownian particle which is obtained in the precise mathematical form of a limit inequality. These quantitative results can help to properly apply the theories associated with Brownian-particle modelling. The consideration also discusses a series of works of other authors.

scholarly journals Brownian motion of black holes in stellar systems with non-Maxwellian distribution of the field stars

2006 ◽  
Vol 2 (S238) ◽  
pp. 427-428
Author(s):  
Isabel Tamara Pedron ◽  
Carlos H. Coimbra-Araújo
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Distribution Function ◽  
Brownian Motion ◽  
Random Walk ◽  
Brownian Particle ◽  
Stellar System ◽  
Stellar Systems ◽  
Massive Black Hole ◽  
Nearby Stars

AbstractA massive black hole at the center of a dense stellar system, such as a globular cluster or a galactic nucleus, is subject to a random walk due gravitational encounters with nearby stars. It behaves as a Brownian particle, since it is much more massive than the surrounding stars and moves much more slowly than they do. If the distribution function for the stellar velocities is Maxwellian, there is a exact equipartition of kinetic energy between the black hole and the stars in the stationary state. However, if the distribution function deviates from a Maxwellian form, the strict equipartition cannot be achieved.The deviation from equipartition is quantified in this work by applying the Tsallis q-distribution for the stellar velocities in a q-isothermal stellar system and in a generalized King model.

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