Arguments recently proposed by Kranyš concerning the nondistinguishability between Abraham's and Minkowski's electromagnetic contributions to the total energy-momentum tensor of the same relativistic, thermodynamically closed system are extended to other electromagnetic energy-momentum tensors (as proposed by Grot and Eringen and de Groot and Suttorp). The adjustment of the corresponding "matter" contribution, which occurs in each element of the canonical space-time decomposition of the total energy-momentum tensor, is exhibited in those different cases. For dissipation-free systems this adjustment can be achieved for each case by means of an ad hoc Legendre transformation on the internal energy density. The arguments used do not presuppose any isotropy and linearity of the medium and can be readily extended to the cases of media with hysteresis and media endowed with intrinsic spins, be they of a fluid-like or solid-like type of mechanical behavior.
Maxwell's equations in Minkowski's world: their premetric generalization and the electromagnetic energy-momentum tensor