Related papers: Teaching the Principles of Statistical Dynamics
The Arcsine laws of Brownian motion are a collection of results describing three different statistical quantities of one-dimensional Brownian motion: the time at which the process reaches its maximum position, the total time the process…
We introduce a novel linear transport equation that models the evolution of a one-particle distribution subject to free transport and two distinct scattering mechanisms: one affecting the particle's speed and the other its direction. These…
Depending on context, the term entropy is used for a thermodynamic quantity, a~measure of available choice, a quantity to measure information, or, in the context of statistical inference, a maximum configuration predictor. For systems in…
Statistical thermodynamics delivers the probability distribution of the equilibrium state of matter through the constrained maximization of a special functional, entropy. Its elegance and enormous success have led to numerous attempts to…
We generalize Einstein's probabilistic method for the Brownian motion to study compressible fluids in porous media. The multi-dimensional case is considered with general probability distribution functions. By relating the expected…
We derive a stochastic wave equation for an inflaton in an environment of an infinite number of fields. We study solutions of the linearized stochastic evolution equation in an expanding universe. The Fokker-Planck equation for the inflaton…
Stochastic thermodynamics provides a framework for describing small systems like colloids or biomolecules driven out of equilibrium but still in contact with a heat bath. Both, a first-law like energy balance involving exchanged heat and…
This paper explores the possibility that asset prices, especially those traded in large volume on public exchanges, might comply with specific physical laws of motion and probability. The paper first examines the basic dynamics of asset…
The statistical mechanical description of two-dimensional inviscid fluid turbulence is reconsidered. Using this description, we make predictions about turbulent flow in a rapidly rotating laboratory annulus. Measurements on the continuously…
In a growing number of strongly disordered and dense systems, the dynamics of a particle pulled by an external force field exhibits super-diffusion. In the context of glass forming systems, super cooled glasses and contamination spreading…
This note outlines a mean-field approach to dynamic optimal transport problems based on the recently proposed McKean-Pontryagin maximum principle. Key aspects of the proposed methodology include i) avoidance of sampling over stochastic…
An unified thermodynamical framework based in the use of a generalized Massieu-Planck thermodynamic potential is proposed and a new formulation of Boltzmann-Gibbs Statistical Mechanics is established. Under this philosophy a generalization…
We study the statistics of a tagged particle in single-file diffusion, a one-dimensional interacting infinite-particle system in which the order of particles never changes. We compute the two-time correlation function for the displacement…
I give a concise introduction to some essential concepts of statistical mechanics: 1. Probability theory (constrained distributions, concentration theorem, frequency estimation, hypothesis testing); 2. Macroscopic systems in equilibrium…
We analyze a pair of diffusion equations which are derived in the infinite system--size limit from a microscopic, individual--based, stochastic model. Deviations from the conventional Fickian picture are found which ultimately relate to the…
Particle flows injected as beams and scattered by an intruder are numerically studied. We find a crossover of the drag force from Epstein's law to Newton's law, depending on the ratio of the speed to the thermal speed. These laws can be…
In this paper, we study the long-time behavior of a fluid particle immersed in a turbulent fluid driven by a diffusion with jumps, that is, a Feller process associated with a non-local operator. We derive the law of large numbers and…
We show that by integrating out the electric field and incorporating proper boundary conditions, a semiclassical Boltzmann equation can describe electron transport properties, continuously from the diffusive to ballistic regimes. General…
The purpose of this note is to see to what extent ideal gas laws can be obtained from simple Newtonian mechanics, specifically elastic collisions. We present simple one-dimensional situations that seem to validate the laws. The first…
Using statistical thermodynamics, we derive a general expression of the stationary probability distribution for thermodynamic systems driven out of equilibrium by several thermodynamic forces. The local equilibrium is defined by imposing…