  We study the effect of intrinsic noise on the thermodynamic balance of
complex chemical networks subtending cellular metabolism and gene regulation. A
topological network property called deficiency, known to determine the
possibility of complex behavior such as multistability and oscillations, is
shown to also characterize the entropic balance. In particular, only when
deficiency is zero does the average stochastic dissipation rate equal that of
the corresponding deterministic model, where correlations are disregarded. In
fact, dissipation can be reduced by the effect of noise, as occurs in a toy
model of metabolism that we employ to illustrate our findings. This phenomenon
highlights that there is a close interplay between deficiency and the
activation of new dissipative pathways at low molecule numbers.
