Revisiting relativistic magnetohydrodynamics from quantum electrodynamics

We provide a statistical mechanical derivation of relativistic magnetohydrodynamics on the basis of (3 + 1)-dimensional quantum electrodynamics; the system endowed with a magnetic one-form symmetry. The conservation laws and 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 a thermodynamic functional enables us to obtain exact forms of constitutive relations. Applying the derivative expansion to exact formulas, we derive the first-order constitutive relations for nonlinear relativistic magnetohydrodynamics. Our results for the QED plasma preserving parity and charge-conjugation symmetries are 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 semi-positivity of the entropy production rate consistent with the local second law of thermodynamics.

Automated summary

This study presents a statistical mechanical derivation of relativistic magnetohydrodynamics based on (3 + 1)-dimensional quantum electrodynamics, showcasing the covariance of conservation laws and constitutive relations with respect to general coordinate transformations. By using the local Gibbs ensemble method and derivative expansion, exact constitutive relations are obtained for nonlinear relativistic magnetohydrodynamics. The results indicate the existence of electrical resistivities and viscosities, while satisfying Onsager's reciprocal relation and a set of inequalities consistent with the local second law of thermodynamics.