  A reduced chemical scheme involving a small number of variables is often
sufficient to account for the deterministic evolution of the concentrations of
the main species contributing to a reaction. However its predictions are
questionable in small systems used for example in fluorescence correlation
spectroscopy (FCS) or in explosive systems involving strong nonlinearities such
as autocatalytic steps. We make precise dynamical criteria defining the
validity domain of the quasi-steady-state approximation and the elimination of
a fast concentration in deterministic dynamics. Designing two different
three-variable models converging toward the same two-variable model, we show
that the variances and covariance of the fluctuations of the slow variables are
not correctly predicted by the two-variable model, even in the limit of a large
system size. The more striking weaknesses of the reduced scheme are figured out
in mesoscaled systems containing a small number of molecules. The results of
two stochastic approaches are compared and the shortcomings of the Langevin
equations with respect to the master equation are pointed out. We conclude that
the description of the fluctuations and their coupling with nonlinearities of
deterministic dynamics escape reduced chemical schemes.
