For example, any chemically sound reaction model will implicitly forbid pathways that transform N 2O into H 2O. This is not always possible in real reaction networks where the transformations are constrained by stoichiometry of chemical constituents. Our basic assumption is that the network is able to transform the two boundary species into each other. In the following, we will call the chemical species that are kept constant ‘boundary species’, because they are the species to which the boundary conditions are applied to. The environment is driving the network to thermodynamic disequilibrium by keeping the concentration of two species constant. We look at reaction networks as thermodynamic systems that transforms two chemical species into one another. Possible applications of this approach include the thermodynamic investigation of reaction models in biology, origin of life and also Earth system and planetary science. This might contribute to a framework that allows to test methods for reconstructing thermodynamic data of reaction networks and lead to a better thermodynamic understanding of reaction networks in general. Here, we extend their study by generating big random linear and nonlinear reaction networks and simulating them to a thermodynamically constrained steady state. In 2006 Cantú and Nicolis studied thermodynamic properties of linear networks, but limited themselves to small networks, which they were able to handle analytically. Despite the fact that the terms were used in combination, the theory was merely a graphical representation of conservation equations and did not make any statements about complex networks, as they are known today. We conclude that the relation between distribution of dissipation, network topology and strength of disequilibrium is nontrivial and can be studied systematically by artificial reaction networks.Ĭonnecting network theory with thermodynamics was an idea already present more than 40 years ago under the term network thermodynamics. Increasing the flow through the nonlinear networks also increases the number of cycles and leads to a narrower distribution of chemical potentials. This effect is stronger in nonlinear networks than in the linear ones. An elevated entropy production rate is found in reactions associated with weakly connected species. The distribution of entropy production of the individual reactions inside the network follows a power law in the intermediate region with an exponent of circa −1.5 for linear and −1.66 for nonlinear networks. In all networks, the flow decreases with the distance between the inflow and outflow boundary species, with Watts-Strogatz networks showing a significantly smaller slope compared to the three other network types. For similar boundary conditions the steady state flow through the linear networks is about one order of magnitude higher than the flow through comparable nonlinear networks. We generate linear and nonlinear networks using four different complex network models (Erdős-Rényi, Barabási-Albert, Watts-Strogatz, Pan-Sinha) and compare their topological properties with real reaction networks. To circumvent the problem of sparse thermodynamic data, we generate artificial reaction networks and investigate their non-equilibrium steady state for various boundary fluxes. Despite the importance of thermodynamic disequilibrium for many of those systems, the general thermodynamic properties of reaction networks are poorly understood. Reaction networks are useful for analyzing reaction systems occurring in chemistry, systems biology, or Earth system science.
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