 
Summary: Statistical mechanical theory for steady state systems.
VII. Nonlinear theory
Phil Attard
School of Chemistry F11, University of Sydney, New South Wales 2006, Australia
Received 16 January 2007; accepted 9 May 2007; published online 2 July 2007
The second entropy theory for nonequilibrium thermodynamics is extended to the nonlinear regime
and to systems of mixed parity even and odd functions of molecular velocities . The steady state
phase space probability density is given for systems of mixed parity. The nonlinear transport matrix
is obtained and it is shown to yield the analog of the linear OnsagerCasimir reciprocal relations. Its
asymmetric part contributes to the flux and to the production of second entropy. The nonlinear
transport matrix is not simply expressible as a GreenKubo fluctuation equilibrium time correlation
function. However, here the first nonlinear correction to the transport coefficient is given explicitly
as a type of the GreenKubo equilibrium time correlation function. The theory is illustrated by
application to chemical kinetics. © 2007 American Institute of Physics. DOI: 10.1063/1.2745300
I. INTRODUCTION
This is the seventh paper in a series on a theory for
nonequilibrium thermodynamics and statistical
mechanics.16
A selfcontained review of the theory up to the
fifth paper has been given.7
