ABSTRACT
Simple cellular automata which seem to capture the essential features of thermodynamics and hydrodynamics are discussed. Thermodynamics and hydrodynamics describe the overall behaviour of many systems, independent of the precise microscopic construction of each system. One can thus study thermodynamics and hydrodynamics using simple models, which are more amenable to efficient simulation, and potentially to mathematical analysis. Cellular automata (CA) are discrete dynamical systems which give simple models for many complex physical processes. This chapter considers CA which can be viewed as discrete approximations to molecular dynamics. The hydrodynamics of the CA is much like a standard physical fluid. Assuming local equilibrium, the large-scale behaviour of the CA can be approximated by average rules for collections of particles, with particular average densities and velocities. The hexagonal lattice CA is then found to follow exactly the standard Navier-Stokes equations. The chapter gives further evidence that simple cellular automata can reproduce the essential features of thermodynamic and hydrodynamic behaviour.
