Statistical theory of the equilibrium elastic and thermal properties of crystals

A study is made of the equilibrium elastic and thermal properties of a crystal that consists of particles with rotational degrees of freedom. To describe its strain and stress states, asymmetric strain and stress tensors are used. On the basis of microscopic expressions for the strain and stress tensors by means of a local-equilibrium ensemble, statistical expressions are obtained for the specific heat of the deformed medium for fixed strain tensors, for four isothermal tensors of elastic moduli, temperature stress coefficients, and coefficients of thermal expansion. These properties are described by static correlation functions of dynamical quantities.