Coarse grains: the emergence of space and order

Details Coarse grains: the emergence of space and order Coarse grains: the emergence of space and order

2001-02-05

arxiv.org/abs/cond-mat/0102071v1

Found. Phys. 31, 713 - 731 (2001)

Physics

Condensed Matter

Statistical Mechanics

To appear in Foundations of Physics, Festschrift for Martin Gutzwiller

Scientific paper

10.1023/A:1017577211902

The emergence of macroscopic variables can be effected through {\it coarse graining}. Despite practical and fundamental benefits conveyed by this partitioning of state space, the apparently subjective nature of the selection of coarse grains has been considered problematic. We provide objective selection methods, deriving from the existence of relatively slow dynamical time scales. 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 graining, 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.

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