 
Summary: Journal of Chemical Physics 121 (2004) 61676174; Erratum, ibid. 125 (2006) 219902
Fluctuation theorem and Onsager reciprocity relations
D. Andrieux and P. Gaspard
Center for Nonlinear Phenomena and Complex Systems,
Universit´e Libre de Bruxelles, Code Postal 231, Campus Plaine, B1050 Brussels, Belgium
The Onsager and higherorder reciprocity relations are derived from a fluctuation theorem for
nonequilibrium reactions ruled by the chemical master equation. The fluctuation theorem is obtained
for the generating function of the macroscopic fluxes between chemiostats maintaining the system
in a nonequilibrium steady state. The macroscopic affinities associated with the fluxes are identified
by graph theory. The YamamotoZwanzig formulas for the reaction constants are also derived from
the fluctuation theorem.
PACS numbers: 82.20.Uv; 05.70.Ln; 02.50.Ey
I. INTRODUCTION
Outofequilibrium systems are characterized by a positive entropy production due to the fluxes of matter and
energy generated by the thermodynamic forces also called the affinities. These forces or affinities arise because of
inhomogeneities in the chemical potentials, the pressure or the temperature. This is the case for systems driven out
of equilibrium at their boundaries by contact with chemiostats. At the statisticalmechanical level of description, the
time evolution can be considered as a Markovian stochastic process ruled by a master equation for the probability
distribution of the stochastic variables which are the number of molecules of the intermediate species participating
to a nonequilibrium reaction network, as proposed by Nicolis and coworkers.17
