Thermodynamics of polarized relativistic matter

TL;DR

This paper derives the free energy and related physical quantities of polarized relativistic matter in external fields, clarifying the role of polarization and its effects in equilibrium.

Contribution

It provides a systematic derivation of the free energy and energy-momentum tensor for polarized relativistic matter, including ambiguities and physical effects of polarization.

Findings

Explicit expression for free energy in external fields.

Relation between polarization and bound currents/momenta.

Identification of ambiguities in polarization vectors.

Abstract

We give the free energy of equilibrium relativistic matter subject to external gravitational and electromagnetic fields, to one-derivative order in the gradients of the external fields. The free energy allows for a straightforward derivation of bound currents and bound momenta in equilibrium. At leading order, the energy-momentum tensor admits a simple expression in terms of the polarization tensor. Beyond the leading order, electric and magnetic polarization vectors are intrinsically ambiguous. The physical effects of polarization, such as the correlation between the magneto-vortically induced surface charge and the electro-vortically induced surface current, are not ambiguous.