Stability of multi-component Israel-Stewart-Maxwell theory for charge diffusion

We obtain stability criteria for diffusive inviscid multi-component Israel-Stewart hydrodynamics with and without background or dynamic electromagnetic fields. Our analysis is grounded on the maximum entropy principle, and it provides stability conditions that are valid around all thermodynamic equilibria, including rotating equilibria, charged equilibria, and equilibria in a background gravitational field. We prove that the electromagnetic part of the information current is stable and causal by construction and, therefore, the stability criteria found for Israel-Stewart theories of hydrodynamics automatically extend to similar formulations of magnetohydrodynamics.