The stress tensor in Thermodynamics and Statistical Mechanics

We prove that the stress tensor,τab, of a molecular system with arbitrary, short-range interactions can be point-wisely expressed as the functional derivative of the partition function with respect to the local deformation tensor. In this approach, the set of components of τab has a simple interpretation as the set of Lagrangian multipliers which one needs to introduce to enforce the conditions relating point particle displacements to the body local deformation tensor. The question of the possible nonuniqueness of the formula for τab is discussed.