Lorentz covariant statistical mechanics and thermodynamics of the relativistic ideal gas and preferred frame

The Lorentz covariant classical and quantum statistical mechanics and thermodynamics of an ideal relativistic gas of bradyons (particles slower than light), luxons (particles moving with the speed of light) and tachyons (hypothetical particles faster than light) is discussed. The Lorentz covariant formulation is based on the preferred frame approach which among others enables consistent, free of paradoxes description of tachyons. The thermodynamic functions within the covariant approach are obtained both in classical and quantum case.