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Deformed quantum statistics in two-dimensions

It is known from the early work of May in 1964 that ideal Bose gas do not exhibit condensation phenomenon in two dimensions. On the other hand, it is also known that the thermostatistics arising from q-deformed oscillator algebra has no connection with the spatial dimensions of the system. Our recent work concerns the study of important thermodynamic functions such as the entropy, occupation number, internal energy and specific heat in ordinary three spatial dimensions, where we established that such thermostatistics is developed by consistently replacing the ordinary thermodynamic derivatives by the Jackson derivatives. The thermostatistics of q-deformed bosons and fermions in two spatial dimensions is an unresolved question and that is the subject of this investigation. We study the principal thermodynamic functions of both bosons and fermions in the two dimensional q-deformed formalism and we find that, different from the standard case, the specific heat of q-boson and q-fermion ideal gas, at fixed temperature and number of particle, are no longer identical.