A kinetics built upon $q$-calculus, the calculus of discrete dilatations, is
shown to describe diffusion on a hierarchical lattice. The only observable on
this ultrametric space is the "quasi-position" whose eigenvalues are the levels
of the hierarchy, corresponding to the volume ofphase space available to the
system at any given time. Motion along the lattice of quasi-positions is
irreversible.Comment: 15 pages, 2 figures, Revtex formatte
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