 
Summary: Statistical mechanical theory for steady state systems. VIII. General theory
for a Brownian particle driven by a time and spacevarying force
Phil Attarda
and Angus GrayWeale
School of Chemistry F11, University of Sydney, Sydney NSW 2006, Australia
Received 2 November 2007; accepted 14 January 2008; published online 21 March 2008
A Brownian particle subject to a time and spacevarying 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
timevarying 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.
© 2008 American Institute of Physics. DOI: 10.1063/1.2839883
I. INTRODUCTION
Brownian motion is the archetype for a stochastic pro
cess: The evolution in time of a system subject to determin
