Thermodynamic pressure and mechanical pressure for electromagnetic media

TL;DR

This paper clarifies the differences between thermodynamic and mechanical pressures in electromagnetic media, emphasizing their tensor nature and the conditions under which scalar approximations are valid.

Contribution

It distinguishes between thermodynamic and mechanical pressures in electromagnetic media and discusses their tensor properties and scalar approximations for simple media.

Findings

Mechanical and thermodynamic pressures differ in electromagnetic media.

Both pressures are fundamentally tensor quantities.

Scalar theory suffices for simple media under certain conditions.

Abstract

By the mechanical pressure we mean that the pressure in the fundamental thermodynamic equation with the naive form of the electromagnetic work used, while the thermodynamic one we mean that in the equation with proper thermodynamic form of the electromagnetic work instead. Both pressures differ from a magnetic mutual field pressure which results from the electromagnetic stress tensor for the linear and uniform media in static electromagnetic field. Both pressures are in essence tensors, but a quasi-scalar theory is sufficient for the simple media.