Abstract
The emergence of macroscopic variables can be effected through 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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One can carry this perspective to its logical extreme, perhaps leading to a physics analog of the remark of L. Mies van der Rohe, “God is in the details” New York Herald Tribune, 28 June 1959).
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Schulman, L.S., Gaveau, B. Coarse Grains: The Emergence of Space and Order. Foundations of Physics 31, 713–731 (2001). https://doi.org/10.1023/A:1017577211902
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DOI: https://doi.org/10.1023/A:1017577211902