The stress tensor in Thermodynamics and Statistical Mechanics

Abstract

We prove that the stress tensor, tau^{ab}, 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 tau^{ab} has a simple interpretation as the set of Lagrangian multipliers which need to be introduced to enforce the conditions relating point particle displacements to the body local deformation tensor. The question of the non-uniqueness of the formula for tau^{ab} is discussed.