  The problem of anisotropic pressures arising as a consequence of the spatial
symmetry breaking introduced by an external magnetic field in quantum systems
is discussed. The role of the conservation of energy and momentum of external
fields as well as of systems providing boundary conditions in quantum
statistics is considered. The vanishing of the average transverse momentum for
an electron-positron system in its Landau ground state is shown, which means
the vanishing of its transverse pressure. The situation for neutron case and
Strange Quark Matter (SQM) in $\beta$-equilibrium is also briefly discussed.
Thermodynamical relations in external fields as well as the form of the stress
tensor in a quantum relativistic medium are also discussed. The ferromagnetic
symmetry breaking is briefly discussed.
