Thermodynamic Limit from Small Lattices of Coupled Maps

We compare the behavior of a small truncated coupled map lattice with random inputs at the boundaries with that of a large deterministic lattice essentially at the thermodynamic limit. We find exponential convergence for the probability density, predictability, power spectrum, and two-point correlation with increasing truncated lattice size. This suggests that spatiotemporal embedding techniques using local observations cannot detect the presence of spatial extent in such systems and hence they may equally well be modeled by a local low dimensional stochastically driven system.