Geometric approach to the pressure tensor and the elastic constants

Expressions are obtained for the pressure tensor in the canonical and the microcanonical ensemble for both isolated and periodic systems, using the same geometric approach to thermodynamic derivatives as has been used previously to define the configurational temperature. The inherent freedom of the method leads to a straightforward proof of the equivalence of atomic and molecular pressures, for short molecules and for molecules exceeding the dimensions of a periodic simulation box. The effect of holonomic constraints on the pressure is discussed. Expressions for the elastic constants are derived in the same manner.