A perspective on the microscopic pressure (stress) tensor: history, current understanding, and future challenges

TL;DR

This paper reviews the history, current methods, and future challenges in defining and calculating the microscopic pressure tensor across various scientific fields, highlighting unresolved issues and potential research directions.

Contribution

It provides a comprehensive overview of methods to compute the microscopic pressure tensor and discusses key challenges and future research directions in the field.

Findings

Connections between equilibrium and non-equilibrium pressure forms established

Identification of key challenges like many-body potentials and measurement difficulties

Suggestions for future research directions in microscopic pressure tensor studies

Abstract

The pressure tensor (equivalent to the negative stress tensor) at both microscopic and macroscopic levels is fundamental to many aspects of engineering and science, including fluid dynamics, solid mechanics, biophysics, and thermodynamics. In this perspective paper, we review methods to calculate the microscopic pressure tensor. Connections between different pressure forms for equilibrium and non-equilibrium systems are established. We also point out several challenges in the field, including the historical controversies over the definition of the microscopic pressure tensor; the difficulties with many-body and long-range potentials; the insufficiency of software and computational tools; and the lack of experimental routes to probe the pressure tensor at the nanoscale. Possible future directions are suggested.