I always had a problem understanding coarse-graining: Macroscopic state variables such as Temperature represent, say aggregate molecule speeds within cells that are homogenous enough in character at a certain coarseness of scale.
These cells are localised islands of tranquility and we stitch them together. But that very choice of scale implies no equilibrium exists between neighbouring islands; if not why not make the view coarser and broaden the cell?
The cells otherwise are transitioning according to the zeroth law, being in mutual contact as they are at different aggregate temperatures.
So is not one observers coarse-grained view of a system of localised states in static equilibrium another ones view of states still in flux? Equilibrium is scale-dependent?
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