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Quantum dynamics can be regarded as a generalization of classicalfinite-state dynamics. This is a familiar viewpoint for workers in quantumcomputation, which encompasses classical computation as a special case. Herethis viewpoint is extended to mechanics, where classical dynamics hastraditionally been viewed as a macroscopic approximation of quantum behavior,not as a special case.  When a classical dynamics is recast as a special case of quantum dynamics,the quantum description can be interpreted classically. For example, sometimesextra information is added to the classical state in order to construct thequantum description. This extra information is then eliminated by representingit in a superposition as if it were unknown information about a classicalstatistical ensemble. This usage of superposition leads to the appearance ofFermions in the quantum description of classical lattice-gas dynamics and turnscontinuous-space descriptions of finite-state systems into illustrations ofclassical sampling theory.  A direct mapping of classical systems onto quantum systems also allows us todetermine the minimum possible energy scale for a classical dynamics, based ona localized rate of state change. We use a partitioning description of dynamicsto define locality, and discuss the ideal energy of two model systems.

Mechanical Systems that are both Classical and Quantum