The stress tensor in Thermodynamics and Statistical Mechanics

TL;DR

This paper derives a general expression for the stress tensor in molecular systems with short-range interactions, linking it to the partition function and local deformation, and discusses its uniqueness.

Contribution

It provides a novel, general derivation of the stress tensor as a functional derivative of the partition function for arbitrary short-range interactions.

Findings

Stress tensor expressed as functional derivative of partition function

Interpretation of stress tensor components as Lagrangian multipliers

Discussion on the non-uniqueness of the stress tensor formula

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.