  The energy dissipation rate in a nonequilibirum reaction system can be
determined by the reaction rates in the underlying reaction network. By
developing a coarse-graining process in state space and a corresponding
renormalization procedure for reaction rates, we find that energy dissipation
rate has an inverse power-law dependence on the number of microscopic states in
a coarse-grained state. The dissipation scaling law requires self-similarity of
the underlying network, and the scaling exponent depends on the network
structure and the flux correlation. Implications of this inverse dissipation
scaling law for active flow systems such as microtubule-kinesin mixture are
discussed.
