 
Summary: Statistical mechanical theory for steady state systems. II. Reciprocal
relations and the second entropy
Phil Attard
School of Chemistry F11, University of Sydney, New South Wales 2006, Australia
Received 8 December 2004; accepted 25 January 2005; published online 15 April 2005
The concept of second entropy is introduced for the dynamic transitions between macrostates. It is
used to develop a theory for fluctuations in velocity, and is exemplified by deriving Onsager
reciprocal relations for Brownian motion. The cases of free, driven, and pinned Brownian particles
are treated in turn, and Stokes' law is derived. The second entropy analysis is applied to the general
case of thermodynamic fluctuations, and the Onsager reciprocal relations for these are derived using
the method. The GreenKubo formulas for the transport coefficients emerge from the analysis, as do
Langevin dynamics. © 2005 American Institute of Physics. DOI: 10.1063/1.1873572
I. INTRODUCTION
This is the second in a series of papers on the statistical
mechanics of steady state systems. The first paper,1
herein
after referred to as I, gave the structural probability distribu
tion for systems subject to an externally imposed thermody
namic gradient, and presented results for the first energy
moment of a LennardJones fluid that develops in response
