Rigorous classical-mechanical derivation of a multiple-copy algorithm for sampling statistical mechanical ensembles

We derive a rigorous, multiple-copy simulation algorithm that is formally equivalent to conventional classical molecular dynamics for an ensemble of systems, but may be used for rapid geometry optimizations. The derivation is accomplished by starting from an ensemble of copies of the entire system and applying a point coordinate transformation to a large subsystem defined as the bath. After the transformation, each atom of the bath is described by one "major" set of coordinates located at the average position of the ensemble of equivalent atoms and a set of "minor" coordinates that when combined with the "major" coordinates represent exact dynamics. Neglecting the "minor" set of coordinates results in a Hamiltonian and a probability density equivalent to those used in existing multiple-copy methods. Neglecting Hamilton's equations of motion for the minor variables gives the equations of motion for locally enhanced sampling. Numerical tests indicate that the algorithm can recover exact molecular dynamics of the ensemble, conventional multiple-copy dynamics, or results of intermediate accuracy. Thus, the algorithm provides a rigorous basis for multiple-copy dynamics, resolves many of the uncertainties associated with their current implementations, and offers the potential for calculating ensemble average properties in conjunction with finding a system's global minimum energy geometry.