 
Summary: Nonequilibrium Monte Carlo simulation for a driven Brownian particle
Phil Attard
School of Chemistry F11, University of Sydney, New South Wales 2006, Australia
Received 14 July 2009; revised manuscript received 5 September 2009; published 23 October 2009
The author's nonequilibrium probability distribution is tested for timevarying mechanical work. Nonequi
librium Monte Carlo NEMC is used to simulate a Brownian particle in a softsphere solvent, driven by a
moving external potential. Results are obtained for the phase lag and amplitude for drive frequencies ranging
from the steady state to the transient regime. This now extends the application of the NEMC algorithm to a
timevarying nonequilibrium system. The results are shown to agree with those obtained by nonequilibrium
stochastic molecular dynamics and by NoséHoover molecular dynamics, from which it is concluded that the
nonequilibrium probability distribution correctly describes timevarying mechanical work and that it provides
a fundamental basis for nonequilibrium statistical mechanics.
DOI: 10.1103/PhysRevE.80.041126 PACS number s : 05.70.Ln, 05.20. y, 05.40.Jc, 05.10.Ln
I. INTRODUCTION
The Boltzmann distribution for the phasespace probabil
ity is the foundation upon which classical equilibrium statis
tical mechanics is erected. In contrast, there is no consensus
for the form of the probability distribution for nonequilib
rium systems, and, consequently, there is currently no recog
nized foundation upon which to formulate a general theory
