Abstract
This article explores the formulation of evolution equations for atomistic systems where the time resolution is controlled at will. Based on a time-rescaled version of Hamilton’s equations of motion, the equations of motion of these systems are derived with adjustable time granularity. Also, using the Liouville formalism for Hamiltonian mechanics, the evolution equations are recast in probabilistic terms, opening the door to variational, Galerkin-type projections. The resulting approximation provides the governing equations for the average motion of the system as well as the evolution of a temperature-like variable that modulates the thermal, unresolved, vibrations of each particle. The balance between the resolved and unresolved motions is, by construction, adjustable at every instant and fully reversible. This kind of models can be used to study the behavior of atomistic systems at different time scales.
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