Scaling of Energy Dissipation in Nonequilibrium Reaction Networks

TL;DR

This paper derives a scaling law for energy dissipation in nonequilibrium reaction networks, showing it depends inversely on the number of states and is influenced by network structure and flux correlations.

Contribution

It introduces a coarse-graining and renormalization approach to relate energy dissipation to network properties in nonequilibrium systems.

Findings

Energy dissipation scales inversely with the number of microscopic states.

Self-similarity of the network is required for the scaling law.

Scaling exponent depends on network structure and flux correlations.

Abstract

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.