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Brownian motion is a ubiquitous physical phenomenon across the sciences. After its discovery by Brown and intensive study since the first half of the 20th century, many different aspects of Brownian motion and stochastic processes in…
After a general discussion of the thermodynamics of conductive processes, we introduce specific observables enabling the connection of the diffusive transport properties with the microscopic dynamics. We solve the case of Brownian…
Entropic Dynamics is a framework in which dynamical laws are derived as an application of entropic methods of inference. No underlying action principle is postulated. Instead, the dynamics is driven by entropy subject to the constraints…
We derive the asymptotic winding law of a Brownian particle in the plane subjected to a tangential drift due to a point vortex. For winding around a point, the normalized winding angle converges to an inverse Gamma distribution. For winding…
A semiclassical kinetic theory is presented for the fluctuating photon flux emitted by a disordered medium in thermal equilibrium. The kinetic equation is the optical analog of the Boltzmann-Langevin equation for electrons. Vacuum…
We consider a relativistic brane propagating in Minkowski spacetime described by any action which is local in its worldvolume geometry. We examine the conservation laws associated with the Poincar\'e symmetry of the background from a…
In this article we explore the phenomena of nonequilibrium stochastic process starting from the phenomenological Brownian motion. The essential points are described in terms of Einstein's theory of Brownian motion and then the theory…
Brownian motion is ballistic on short time scales and diffusive on long time scales. Our theoretical investigations indicate that one can observe the exact opposite - an "anomaleous diffusion process" where initially diffusive motion…
We consider non-relativistic point-particles coupled to Einstein gravity and their canonical quantization. From the resulting Wheeler-DeWitt wave equation we determine a quantum version of geometrodynamics, where the coupled evolution of…
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…
The stochastic dynamics of an active particle undergoing a constant speed and additionally driven by an overall fluctuating torque is investigated. The random torque forces are expressed by a stochastic differential equation for the angular…
Explicit density expansions of non-equilibrium probability distribution functions for molecular Brownian particle in ideal gas are obtained in original form what visually implies (is exact solution to) the previously established dynamical…
The Brownian motion of a point particle induced by quantum vacuum fluctuations of a massless real scalar field in Einstein's universe is studied. By assuming the small displacement condition, the dispersion in the momentum and position of a…
In quantum experiments the acquisition and representation of basic experimental information is governed by the multinomial probability distribution. There exist unique random variables, whose standard deviation becomes asymptotically…
We show how pilot-wave theory points to new physics, beyond quantum mechanics, in three distinct ways. First, generalised cosmological initial conditions, departing from the Born rule, can lead to observable anomalies in the cosmic…
A particle in a uniformly accelerated motion exhibits Brownian random motions around the classical trajectory due to the coupling to the field vacuum fluctuations. Previous works show that the Brownian random motions satisfy the energy…
We investigate the ensemble and time averaged mean squared displacements for particle diffusion in a simple model for disordered media by assuming that the local diffusivity is both fluctuating in time and has a deterministic average growth…
The role of acceleration in particle physics can provide an alternative method for probing the properties of quantum gravity. To analyze acceleration-induced processes one utilizes the formalism of quantum field theory in curved spacetime.…
This paper proposes an interpretation of quantum mechanics, relying on the time-symmetric stochastic dynamics of quantum particles and on non-classical probability theory. Our main purpose is to demonstrate that the wave function and its…
This is the second step of a program to use anharmonic plane waves as basis set in non-perturbative quantum field theory. The general framework developed previously is applied to quantum electrodynamics. To test the compatibility with…