Quantum-statistical mechanics in the Lorentzian domain

A recently constructed generalised-Boltzmann statistical mechanics (a compl ement to the Daroczy-Tsallis "non-extensive" statistics) is extended into t he quantum domain. We introduce a control parameter kappa, postulate the ge neralised collision integral and derive the generalised Fermi-Dirac and Bos e-Einstein distribution functions for quantum gases in equilibrium. The ana logy to the Boltzmann case proves the validity of the thermodynamic relatio ns. The grand thermodynamic potential assumes a complicated but suggestive form. The generalized Fermi gas has no real zero-temperature states. At T = 0 it becomes the ordinary Fermi gas. This is interpreted as destruction of correlations as T --> 0. The low-temperature dependence of the control par ameter kappa(T) is determined.