  We study the electron-positron vacuum in a strong magnetic field $B$ in
parallel with Casimir effect. Use is made of the energy-momentum tensor, taken
as the zero temperature and zero density limit of the relativistic quantum
statistical tensor. In both magnetic field and Casimir cases it is shown the
arising of anisotropic pressures. In the first case the pressure transversal to
the field $B$ is negative, whereas along $B$ an usual positive pressure arises.
Similarly, in addition to the usual negative Casimir pressure perpendicular to
the plates, the existence of a positive pressure along the plates is predicted.
The anisotropic pressures suggests a flow of the virtual particles in both
cases. By assuming regions of the universe having random orientation of the
lines of force, cosmological consequences are discussed in the magnetic field
case.
