  Motivated by the theory of relativistic hydrodynamic fluctuations we make use
of the Green-Kubo formula to compute the electrical conductivity and the
(second-order) relaxation time of the electric current of an interacting hadron
gas. We use the recently developed transport code SMASH to numerically solve
the coupled set of Boltzmann equations implementing realistic hadronic
interactions. In particular, we explore the role of the resonance lifetimes in
the determination of the electrical relaxation time. As opposed to a previous
calculation of the shear viscosity we observe that the presence of resonances
with lifetimes of the order of the mean-free time does not appreciably affect
the relaxation of the electric current fluctuations. We compare our results to
other approaches describing similar systems, and provide the value of the
electrical conductivity and the relaxation time for a hadron gas at
temperatures between T=60 MeV and T=150 MeV.
