Generalized hydrodynamics of reaction-diffusion systems and dissipative structures

Generalized hydrodynamics (GH) are derived and used to describe a reaction-diffusion system. The derived GH equations are hyperbolic and are shown to be more general and more suitable than the conventional parabolic reaction-diffusion equations, especially in small geometries. These equations are applied to the study of dissipative structures in glycolysis and are solved numerically using the finite-element method. The solution exhibits a multitude of wave and Turing patterns. The time evolution of the calortropy production for the obtained pattern seems to correlate with the increasing complexity of the system.