Resistive dissipative magnetohydrodynamics from the Boltzmann-Vlasov equation

We derive the equations of motion of relativistic, resistive, second-order dissipative magnetohydrodynamics from the Boltzmann-Vlasov equation using the method of moments. We thus extend our previous work [Phys. Rev. D 98, 076009 (2018)], where we only considered the non-resistive limit, to the case of finite electric conductivity. This requires keeping terms proportional to the electric field $E^mu$ in the equations of motions and leads to new transport coefficients due to the coupling of the electric field to dissipative quantities. We also show that the Navier-Stokes limit of the charge-diffusion current corresponds to Ohms law, while the coefficients of electrical conductivity and charge diffusion are related by a type of Wiedemann-Franz law.