  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.
