 
Summary: Theory for nonequilibrium statistical mechanics
Phil Attard*
Received 23rd March 2006, Accepted 8th May 2006
First published as an Advance Article on the web 7th July 2006
DOI: 10.1039/b604284h
This paper reviews a new theory for nonequilibrium statistical mechanics. This gives the non
equilibrium analogue of the Boltzmann probability distribution, and the generalization of entropy
to dynamic states. It is shown that this socalled second entropy is maximized in the steady state,
in contrast to the rate of production of the conventional entropy, which is not an extremum. The
relationships of the new theory to Onsager's regression hypothesis, Prigogine's minimal entropy
production theorem, the Langevin equation, the formula of Green and Kubo, the Kawasaki
distribution, and the nonequilibrium fluctuation and work theorems, are discussed. The theory is
worked through in full detail for the case of steady heat flow down an imposed temperature
gradient. A Monte Carlo algorithm based upon the steady state probability density is
summarized, and results for the thermal conductivity of a LennardJones fluid are shown to be in
agreement with known values. Also discussed is the generalization to nonequilibrium mechanical
work, and to nonequilibrium quantum statistical mechanics. As examples of the new theory two
general applications are briefly explored: a nonequilibrium version of the second law of
thermodynamics, and the origin and evolution of life.
1. Introduction
