Pattern Formation in Chemical Systems

The spontaneous formation of patterns in chemical systems is a phenomenon that is interesting from both the information-theoretic and the thermodynamic perspective. How can a seemingly increase in order, when a spatial pattern is formed, be explained with the second law of thermodynamics as a force that brings systems closer to equilibrium? How can spatial chemical patterns be characterised in terms of information? How can this be related to the thermodynamics of the chemical system? The aim of this chapter is to answer these question, using the information decomposition along with the thermodynamics perspective, both presented in the previous chapters. With this approach, we can derive a continuity equation for information that is determined by the reaction-diffusion dynamics of the chemical system. Due to the connection between the information in a chemical system and the chemical free energy it represents, we can connect the physical or thermodynamic constraints of the pattern formation process to the information characteristics of the system. The formalism is applied to the self-replicating spots system based on the Gray-Scott reaction-diffusion dynamics.