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We study the effect of intrinsic noise on the thermodynamic balance ofcomplex chemical networks subtending cellular metabolism and gene regulation. Atopological network property called deficiency, known to determine thepossibility of complex behavior such as multistability and oscillations, isshown to also characterize the entropic balance. In particular, only whendeficiency is zero does the average stochastic dissipation rate equal that ofthe corresponding deterministic model, where correlations are disregarded. Infact, dissipation can be reduced by the effect of noise, as occurs in a toymodel of metabolism that we employ to illustrate our findings. This phenomenonhighlights that there is a close interplay between deficiency and theactivation of new dissipative pathways at low molecule numbers.

Dissipation in noisy chemical networks: The role of deficiency