Convergence to equilibrium in a class of interacting particle systems evolving in discrete time

Abstract

We conjecture that for a wide class of interacting particle systems evolving in discrete time, namely conservative cellular automata with piecewise linear flow diagram, relaxation to the limit set follows the same power law at critical points. We further describe the structure of the limit sets of such systems as unions of shifts of finite type. Relaxation to the equilibrium resembles ballistic annihilation, with ``defects'' propagating in opposite direction annihilating upon collision.

15 pages, 6 figures

References in corpus (1)

• A class of cellular automata equivalent to deterministic particle systems

Cited by in corpus (5)

• Cellular Automata Models of Road Traffic
• Probabilistic cellular automata with conserved quantities
• A slow-to-start traffic model related to a M/M/1 queue
• Critical behavior of number-conserving cellular automata with nonlinear fundamental diagrams
• Max-plus analysis on some binary particle systems