  In this work we have obtained a higher-derivative Lagrangian for a charged
fluid coupled with the electromagnetic fluid and the Dirac's constraints
analysis was discussed. A set of first-class constraints fixed by noncovariant
gauge condition was obtained. The path integral formalism was used to obtain
the partition function for the corresponding higher-derivative Hamiltonian and
the Faddeev-Popov ansatz was used to construct an effective Lagrangian. Through
the partition function, a Stefan-Boltzmann type law was obtained.
