Fokker–Planck Equation: Long-Time Dynamics in Approach to Equilibrium

Long-time Dynamics in Approach to Equilibrium

We discuss the approach to equilibrium of systems governed by the Fokker-Planck equation. In particular, we focus on problems involving barrier penetration and the associated Kramers’ time. We also describe the connection between stochastic processes and quantum mechanics. Keywards: Fokker-Planck equation; Approach to equilibrium; Barrier penetration

Particle-Dynamics Approach to Non-Equilibrium Phenomena

A particle-dynamics simulation is a tool for investigating nonequilibrium phenomena accompanied with hydrodynamic, thermodynamic motions, and even with phase transitions. In this article, several applications of the particledynamics simulation and a new computational method of particle dynamics are reported.

Long Range Corrections to the Vapor-Liquid Equilibrium and Surface Tension of Methane with NVT Molecular Dynamics Simulations

The Stochastic Liouville Equation and the Approach to Thermal Equilibrium

Some aspects of behaviour of spins in the presence of random molecular motions are discussed. Various theories which deal with the approach of the spin system to thermal equilibrium are reviewed. It is emphasized that two types of description are used. One is the 'p(t) formalism', where the spin behaviour of one randomly moving molecule is considered. The other is the '(Q) formalism', where the...

Approach to equilibrium for a forced Burgers equation

We show that approach to equilibrium in certain forced Burgers equations is implied by a decay estimate on a suitable intrinsic semigroup estimate, and we verify this estimate in a variety of cases including a periodic force.