Related papers: Corrections to Einstein's relation for Brownian mo…
We presented a methodology to approximate the entropy production for Brownian motion in a tilted periodic potential. The approximation stems from the well known thermodynamic uncertainty relation. By applying a virial-like expansion, we…
Our Recent advancements in stochastic processes have illuminated a paradox associated with the Einstein model of Brownian motion. The model predicts an infinite propagation speed, conflicting with the second law of thermodynamics. The…
In this paper we present a systematic and rigorous method for calculating the diffusion tensor for a Brownian particle moving in a periodic potential which is valid in arbitrary dimensions and for all values of the dissipation. We use this…
In the first paper of this series, I investigated whether a wavefunction model of a heavy particle and a collection of light particles might generate "Brownian-Motion-Like" trajectories of the heavy particle. I concluded that it was…
The diffusive motion of overdamped Brownian particles in tilted piecewise linear pontentials is considered. It is shown that the enhancement of diffusion coefficient by an external static force is quite sensitive to the symmetry of periodic…
Diffusive transport properties of a quantum Brownian particle moving in a tilted spatially periodic potential and strongly interacting with a thermostat are explored. Apart from the average stationary velocity, we foremost investigate the…
The one-dimensional overdamped Brownian motion in a symmetric periodic potential modulated by external time-reversible noise is analyzed. The calculation of the effective diffusion coefficient is reduced to the mean first passage time…
Einstein's theory of Brownian motion is revisited in order to formulate generalized kinetic theory of anomalous diffusion. It is shown that if the assumptions of analyticity and the existence of the second moment of the displacement…
The Einstein-Cartan-Saa theory of torsion modifies the spacetime volume element so that it is compatible with the connection. The condition of connection compatibility gives constraints on torsion, which are also necessary for the…
Recently, dispersionless (coherent) motion of (noninteracting) massive Brownian particles, at intermediate time scales, was reported in a sinusoidal potential with a constant tilt. The coherent motion persists for a finite length of time…
We compute the effective diffusion coefficient of a Brownian particle in a piece-wise linear periodic potential and subject of spatially inhomogeneous temperature, otherwise known as the B{\"u}ttiker-Landauer motor. We obtain analytical…
We consider the degenerate Einsteins Brownian motion model when the time interval of the moving particles before the collisions, is reciprocal to the number of particles per unit volume u(x,t), at the point of observation x at time t. The…
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…
The relativistic generalization of a free Brownian motion theory is presented. The global characteristics of the relaxation are {\it explicitly} found for the velocity and momentum (stochastic) kinetics. It is shown that the thermal…
It is well-known under the name of `periodic homogenization' that, under a centering condition of the drift, a periodic diffusion process on R^d converges, under diffusive rescaling, to a d-dimensional Brownian motion. Existing proofs of…
We discuss a family of time-inhomogeneous two-dimensional diffusions, defined over a finite time interval $[0,T]$, having transition density functions that are expressible in terms of the integral kernels for negative exponentials of the…
We study the problem of lateral diffusion on a static, quasi-planar surface generated by a stationary, ergodic random field possessing rapid small-scale spatial fluctuations. The aim is to study the effective behaviour of a particle…
One century after Einstein's work, Brownian Motion still remains both a fundamental open issue and a continous source of inspiration for many areas of natural sciences. We first present a discussion about stochastic and deterministic…
In this paper, we compare the solutions of Dyson Brownian motion with general $\beta$ and potential $V$ and the associated McKean-Vlasov equation near the edge. Under suitable conditions on the initial data and potential $V$, we obtain the…
We develop an effective theory for biased tracers formulated at the level of the Boltzmann equation, providing a unified description of density and velocity bias. We introduce a general effective collision term in the tracer Boltzmann…