Coarse grains: The emergence of space and order

The emergence of macroscopic variables can be effected through coarse grain ing. Despite practical and fundamental benefits conveyed by this Partitioni ng of state space, the apparently subjective nature of the selection of coa rse grains has been considered problematic. We provide objective selection methods, deriving from the existence of relatively slow dynamical time scal es. Using a framework for nonequilibrium statistical mechanics developed by us, we show the emergence of both spatial variables and order parameters. Although significant objective criteria are introduced in the coarse graini ng, we do not provide a unique prescription. Most significantly, the grains , and by implication entropy, are only defined modulo a characteristic time scale of observation.