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Revisiting relativistic magnetohydrodynamics from quantum electrodynamics

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.