Entropy Production in Chemical Reaction Networks Far from Equilibrium

Abstract

Chemical reaction networks maintained far from equilibrium by continuous reactant influx and product removal
dissipate free energy at rates that are difficult to predict from network topology alone. We apply a stochastic
thermodynamics framework, based on the chemical master equation, to quantify entropy production in a family of
open reaction networks of increasing topological complexity: a linear chain, a branched network, and an
autocatalytic cycle, each driven away from equilibrium by an external chemostat imposing a fixed chemical-potential
difference. Across 36 driving conditions spanning affinities from 0.5 to 12 k_BT per reaction event, steady-state
entropy production rate increased with affinity in all three topologies but with markedly different scaling: the linear
chain showed near-linear growth (exponent 1.04 ± 0.06), the branched network showed mild superlinear growth
(exponent 1.31 ± 0.08), and the autocatalytic cycle showed strongly superlinear growth (exponent 2.18 ± 0.11),
reaching a maximum dissipation rate of 47.3 k_BT per second at the highest affinity tested, 6.4 times higher than
the linear chain at the same driving. Fluctuation analysis using 2.4 x 10^5 stochastic simulation trajectories per
condition confirmed that the steady-state entropy production rate satisfied the integral fluctuation theorem to within
2.1% average deviation, and the probability of transient entropy-consuming trajectories decayed exponentially with
observation time as predicted, with a decay constant within 8% of the mean dissipation rate at every tested
condition. Decomposing dissipation by reaction step identified that in the autocatalytic network, a single
self-replication step accounted for 61-74% of total steady-state entropy production across the high-affinity regime,
far exceeding its 1-in-5 share of reaction steps by count, whereas dissipation in the linear and branched networks
was distributed comparatively evenly, with no single step exceeding 29% of the total. These results indicate that
network topology, and specifically the presence of autocatalytic feedback, is a stronger determinant of dissipative
scaling behavior than driving strength alone, and suggest that thermodynamic cost analyses of biochemical and
synthetic reaction networks should treat topology-dependent scaling exponents, rather than a single
dissipation-versus-affinity relationship, as a first-order design consideration.