Statistical ensembles and molecular dynamics studies of anisotropic solids

We present a general discussion of the isoenthalpic–isostress molecular dynamics theories of Andersen and Parrinello–Rahman. The Parrinello–Rahman theory is shown to be applicable to the case of nonlinear elasticity if the reference state of zero strain is taken to be the state under zero stress; this brings the theory into accord with the thermodynamics of anisotropic solids for arbitrary values of the strain. For the isoenthalpic–isostress ensemble there is a microcanonical counterpart for which we present fluctuation formulas involving the constant strain specific heat, temperature coefficients of thermodynamic tension, and stiffness coefficients. The use of these various ensembles for the molecular dynamic study of polymorphic transitions in crystals is discussed.