  Methods are presented to evaluate the entropy production rate in stochastic
reactive systems. These methods are shown to be consistent with known results
from nonequilibrium chemical thermodynamics. Moreover, it is proved that the
time average of the entropy production rate can be decomposed into the
contributions of the cycles obtained from the stoichiometric matrix in both
stochastic processes and deterministic systems. These methods are applied to a
complex reaction network constructed on the basis of Roessler's reinjection
principle and featuring chemical chaos.
