Conservation laws in cellular automata

Abstract

A conservation law in a cellular automaton (CA) is the statement of the invariance of a local and additive energy-like quantity. This chapter reviews the basic theory of conservation laws in cellular automata. A general mathematical framework for formulating conservation laws in cellular automata is presented and several characterizations of them are summarized. Computational problems regarding conservation laws (verification and existence problems) are discussed.Microscopic explanations of the dynamics of the conserved quantities in terms of flows and particle flows are explored. The related concept of dissipating energy-like quantities is also addressed.