  Reversible lattice dynamics embody basic features of physics that govern the
time evolution of classical information. They have finite resolution in space
and time, don't allow information to be erased, and easily accommodate other
structural properties of microscopic physics, such as finite distinct state and
locality of interaction. In an ideal quantum realization of a reversible
lattice dynamics, finite classical rates of state-change at lattice sites
determine average energies and momenta. This is very different than traditional
continuous models of classical dynamics, where the number of distinct states is
infinite, the rate of change between distinct states is infinite, and energies
and momenta are not tied to rates of distinct state change. Here we discuss a
family of classical mechanical models that have the informational and energetic
realism of reversible lattice dynamics, while retaining the continuity and
mathematical framework of classical mechanics. These models may help to clarify
the informational foundations of mechanics.
