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Nonlinear molecular dynamics and Monte Carlo algorithms.

Equations of motion for the molecular dynamics simulation of crystals are presented; the atomic degrees of freedom are coupled to a thermal reservoir to control temperature and to an elastic reservoir to control the deformation of the lattice, while satisfying a nonlinear stress-strain relation. The exact treatment of finite deformations of the lattice leads to a formulation of the tensorial virial theorem that accounts for the elastic response of the crystal to an inclusion of a new structural phase