13 - Chemical Reaction Networks

Summary

This chapter starts with a discussion of simple univariate chemical reactions networks emphasizing the need to impose thermodynamically consistent reaction rates. For a linear reaction scheme, the stationary distribution is given analytically as a Poisson distribution. Nonlinear schemes can lead to bistability. For large systems, the stationary solution can be expressed by an effective potential. Two types of Fokker–Planck descriptions are shown to fail in certain regimes. In the thermodynamic limit, the dynamics can be described by a simple rate equation. Entropy production is discussed on the various levels of description. A simple two-dimensional scheme, the Brusselator, can lead to persistent oscillations. Heat and entropy production are identified for an individual reaction event of a general multivariate reaction scheme.