Revisiting relativistic magnetohydrodynamics from quantum electrodynamics

TL;DR

This paper derives relativistic magnetohydrodynamics from quantum electrodynamics using statistical mechanics, revealing detailed constitutive relations and transport coefficients for QED plasma with symmetry considerations.

Contribution

It provides an exact, covariant derivation of relativistic MHD from QED, including explicit transport coefficients and their thermodynamic constraints.

Findings

Derived first-order constitutive relations for relativistic MHD from QED.

Identified transport coefficients including resistivities and viscosities.

Confirmed Onsager reciprocal relations and entropy production inequalities.

Abstract

We provide a statistical mechanical derivation of relativistic magnetohydrodynamics on the basis of the $(3+1)$-dimensional quantum electrodynamics; the system endowed with the magnetic one-form symmetry. The conservation laws and the constitutive relations are presented in a manifestly covariant way with respect to the general coordinate transformation. The method of the local Gibbs ensemble (or nonequilibrium statistical operator) combined with the path-integral formula for the thermodynamic functional enables us to obtain an exact form of the constitutive relations. Applying the derivative expansion to the exact formula, we derive the first-order constitutive relations for the relativistic magnetohydrodynamics. The result for the QED plasma preserving the parity and charge-conjugation symmetries is equipped with two electrical resistivities and five (three bulk and two shear) viscosities. We also show that those transport coefficients satisfy the Onsager's reciprocal relation and a set of inequalities, indicating the semi-positivity of the entropy production rate consistent with the local second law of thermodynamics.