Lattice gas simulations of dynamical geometry in one dimension.

Abstract

We present numerical results obtained using a lattice gas model with dynamical geometry. The (irreversible) macroscopic behaviour of the geometry (size) of the lattice is discussed in terms of a simple scaling theory and obtained numerically. The emergence of irreversible behaviour from the reversible microscopic lattice gas rules is discussed in terms of the constraint that the macroscopic evolution be reproducible. The average size of the lattice exhibits power-law growth with exponent at late times. The deviation of the macroscopic behaviour from reproducibility for particular initial conditions ('rogue states') is investigated as a function of system size. The number of such 'rogue states' is observed to decrease with increasing system size. Two mean-field analyses of the macroscopic behaviour are also presented.