Probabilistic cellular automata with conserved quantities

Details Probabilistic cellular automata with conserved quantities Probabilistic cellular automata with conserved quantities

2003-05-27

arxiv.org/abs/nlin/0305051v1

Nonlinear Sciences

Cellular Automata and Lattice Gases

17 pages, 2 figures

Scientific paper

10.1088/0951-7715/17/1/010

We demonstrate that the concept of a conservation law can be naturally extended from deterministic to probabilistic cellular automata (PCA) rules. The local function for conservative PCA must satisfy conditions analogous to conservation conditions for deterministic cellular automata. Conservation condition for PCA can also be written in the form of a current conservation law. For deterministic nearest-neighbour CA the current can be computed exactly. Local structure approximation can partially predict the equilibrium current for non-deterministic cases. For linear segments of the fundamental diagram it actually produces exact results.

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