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We study the thermodynamics of degenerate electron and charged vector boson gases in very intense magnetic fields. In degenerate conditions of the electron gas, the pressure transverse to the magnetic field B may vanish, leading to a transverse collapse. For W bosons an instability arises because the magnetization diverges at the critical field B(c) = M(2)(W)/e. If the magnetic field is self-consistently maintained, the maximum value it can take is of the order of 2B(c)/3, but in any case the system becomes unstable and collapses.

The statistics of q-oscillators, quons and to some extent, of anyons are studied and the basic differences among these objects are pointed out. In particular, the statistical distributions for different bosonic and fermionic q-oscillators are found for their corresponding Fock space representations in the case when the hamiltonian is identified with the number operator. In this case and for nonrelativistic particles, the single-particle temperature Green function is defined with q-deformed periodicity conditions. The equations of state for nonrelativistic and ultrarelativistic bosonic q-gases in an arbitrary space dimension are found near Bose statistics, as well as the one for an anyonic gas near Bose and Fermi statistics. The first corrections to the second virial coefficients are also evaluated. The phenomenon of Bose-Einstein condensation in the q-deformed gases is also discussed. * ) ICSC

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