Related Experiment Video
Updated: Jul 6, 2026

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
Published on: December 4, 2017
Statistical mechanical theory for steady state systems. VIII. General theory for a Brownian particle driven by a
Phil Attard1, Angus Gray-Weale
1School of Chemistry F11, University of Sydney, Sydney, NSW, Australia. attard@chem.usyd.edu.au
Abstract:
A Brownian particle subject to a time- and space-varying force is studied with the second entropy theory for nonequilibrium statistical mechanics. A fluctuation expression is obtained for the second entropy of the path, and this is maximized to obtain the most likely path of the particle. Two approaches are used, one based on the velocity correlation function and one based on the position correlation function. The approaches are a perturbation about the free particle result and are exact for weak external forces. They provide a particularly simple way of including memory effects in time-varying driven diffusion. The theories are tested against computer simulation data for a Brownian particle trapped in an oscillating parabolic well. They accurately predict the phase lag and amplitude as a function of drive frequency, and they account quantitatively for the memory effects that are important at high frequencies and that are missing in the simplest Langevin equation.
Related Concept Videos
Principle of Linear Impulse and Momentum for a System of Particles
Notably, internal forces between particles, occurring in equal and opposite collinear pairs, cancel out and are not part of the equation of motion. This exclusion simplifies the...
First Law: Particles in Two-dimensional Equilibrium
Newton's first law tells us about the...
Equilibrium Conditions for a Particle
To understand the concept of equilibrium, let us first consider the forces acting on an object. When different forces act on an object, they can...
First Law: Particles in One-dimensional Equilibrium
Mechanical Systems
Basic Postulates of Kinetic Molecular Theory: Particle Size, Energy, and Collision
