  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.
