 
Summary: Statistical mechanical theory for nonequilibrium systems. X. Nonequilibrium
phase transitions
Phil Attarda
School of Chemistry F11, University of Sydney, New South Wales 2006 Australia
Received 11 September 2009; accepted 16 October 2009; published online 13 November 2009
A general theory for the stability and coexistence of nonequilibrium phases is formulated. An
integral formulation of the second entropy is given, the functional maximization of which yields
nonlinear hydrodynamics. RayleighBénard convection is analyzed, and analytic approximations
are obtained for the second entropy for conduction and for convection. Despite the simplicity of the
model, coexistence is predicted for a Rayleigh number within 5% of the known value. © 2009
American Institute of Physics. doi:10.1063/1.3259194
I. INTRODUCTION
Equilibrium phase transitions are important in almost all
areas of science, and it is the understanding, quantitative pre
diction, and control of them that underpin many areas of
modern industry and technology. Equilibrium phases are
characterized by their free energy, with the stable phase be
ing the one with lower free energy and phase coexistence
being determined by equality of their free energies. This is
the same as maximizing the total first entropy, as demanded
