Related papers: Einstein's random walk and thermal diffusion
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…
We study the Brownian motion of a classical particle in one-dimensional inhomogeneous environments where the transition probabilities follow quasiperiodic or aperiodic distributions. Exploiting an exact correspondence with the…
We study the one-dimensional diffusion process which takes place between two reflecting boundaries and which is acted upon by a time-dependent and spatially-constant force. The assumed force possesses both the harmonically oscillating and…
We consider random walks on the infinite cluster of a conditional bond percolation model on the infinite ladder graph. In a companion paper, we have shown that if the random walk is pulled to the right by a positive bias $\lambda > 0$, then…
A detailed description of the statistical distribution of thermal vacancies near the melting point is presented, using copper as an example. As the temperature is increased, the average number of thermal vacancies generated by atoms…
Rolling of a small sphere on a solid support is governed by a non-linear friction that is akin to the Coulombic dry fiction. No motion occurs when the external field is weaker than the frictional resistance. However, with the intervention…
We study the three-dimensional persistent random walk with drift. Then we develop a thermodynamic model that is based on this random walk without assuming the Boltzmann-Gibbs form for the equilibrium distribution. The simplicity of the…
We present a model for variations in atmospheric temperature from time scales of one day to one million years based on a stochastic diffusion (random walk) model of the turbulent transport of heat energy vertically in a coupled…
This paper studies particle propagation in a one-dimensional inhomogeneous medium where the laws of motion are generated by chaotic and deterministic local maps. Assuming that the particle's initial location is random and uniformly…
The paper analyzes the phenomenon of turbulent thermal diffusion in the Earth atmosphere, its relation to the turbulent diffusion and its potential impact on aerosol distribution. This phenomenon was predicted theoretically more than 10…
In many physical situations in which many-body assemblies exist at temperature $T$, a characteristic quantum-mechanical time scale of approximately $\hbar/k_{B}T$ can be identified in both theory and experiment, leading to speculation that…
Realistic phenomena can be described more appropriately using generalized canonical ensemble, with proper parameter sets involved. We have generalized the Einstein's theory for specific heat of solid in Tsallis statistics, where the…
We demonstrate that the Einstein relation for the diffusion of a particle in the random energy landscape with the Gaussian density of states is an exclusive 1D property and does not hold in higher dimensions. We also consider the analytical…
Nonequilibrium thermodynamics has shown its applicability in a wide variety of different situations pertaining to fields such as physics, chemistry, biology, and engineering. As successful as it is, however, its current formulation…
It has been shown previously, that the spatial thermal variation of a thermal medium can be recast as a variation in the Euclidean metric. It is now extended to temporal variations in temperature, for a non-relativistic thermal bath, which…
Lateral diffusion of molecules on surfaces plays a very important role in various biological processes, including lipid transport across the cell membrane, synaptic transmission and other phenomena such as exo- and endocytosis, signal…
This paper is a companion to 'Quantum Diffusion with Drift and the Einstein Relation I' (jointly submitted to arXiv). Its purpose is to describe and prove a certain number of technical results used in 'Quantum Diffusion with Drift and the…
In this article, we consider the speed of the random walks in a (uniformly elliptic and i.i.d.) random environment (RWRE) under perturbation. We obtain the derivative of the speed of the RWRE w.r.t. the perturbation, under the assumption…
In this work, energy distribution and thermodynamics are investigated in the Schwarzschild black hole spacetime when considering corrections due to quantum vacuum fluctuations. The Einstein and M{\o}ller prescriptions were used to derive…
Quantum walks are known to propagate quadratically faster than their classical counterparts and are used to model dynamics in various quantum systems. The spread of the quantum walk in position space shows anomalous diffusion behavior. By…