= Coarse-grained variable
A <coarse-grained variable> retains selected collective information while averaging over microscopic details. Dividing a magnetic sample into small cells and assigning each cell its mean <magnetization> gives a field that ignores individual <spins> but still describes variations over many lattice sites. The cell size should be specified relative to both microscopic spacing and the spatial changes of interest.
Different <microstates> can give the same <coarse-grained variable>. At <thermal equilibrium>, their statistical weights contribute an entropic term to the effective <free energy>; the effective cost is therefore not simply the microscopic <energy> evaluated at a smoothed configuration. In <statistical field theory>, a local <order parameter> is a common retained variable. Changing the averaging scale can change its effective parameters while leaving long-distance predictions consistent. Coarse graining is useful precisely because the retained field answers a chosen macroscopic question without reconstructing every microscopic coordinate.
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