Lattice-gas simulations of dynamical geometry in one dimension

TL;DR

This paper investigates the macroscopic evolution of a one-dimensional lattice-gas model with dynamical geometry, revealing power-law growth and the impact of initial conditions on reproducibility, supported by numerical and mean-field analyses.

Contribution

It introduces numerical and mean-field analyses of a dynamical geometry lattice-gas model, highlighting the emergence of irreversible behavior from reversible microscopic rules.

Findings

Lattice size grows as a power law with exponent 1/2 at late times.

Number of rogue states decreases as system size increases.

Reproducibility of macroscopic evolution is affected by initial conditions.

Abstract

We present numerical results obtained using a lattice-gas model with dynamical geometry defined by Hasslacher and Meyer (Int. J. Mod. Phys. C. 9 1597 (1998)). 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 1/2 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.