  Non-ideal fluids are likely to be affected by the occurrence of pressure
anisotropy effects, whose understanding for relativistic systems requires
knowledge of the energy-momentum tensor. In this paper the case of magnetized
jet plasmas at equilibrium is considered, in which both microscopic velocities
of constituent particles as well as the continuum fluid flow are treated as
relativistic ones. A theoretical framework based on covariant statistical
kinetic approach is implemented, which permits the proper treatment of
single-particle and phase-space kinetic constraints and, ultimately, the
calculation of the system continuum fluid fields associated with physical
observables. A Gaussian-like solution for the kinetic distribution function
(KDF) is constructed, in which the physical mechanism responsible for the
generation of temperature anisotropy is identified with magnetic moment
conservation. A Chapman-Enskog representation of the same KDF is then obtained
in terms of expansion around an equilibrium isotropic Juttner distribution.
This permits the analytical calculation of the fluid 4-flow and stress-energy
tensor and the consequent proof that the corresponding kinetic pressure tensor
is non-isotropic. As a notable result, the validity of a polytropic
representation for the perturbative non-isotropic pressure contributions is
established, whereby directional pressures exhibit specific power-law
functional dependences on fluid density.
