Critique of Q-entropy for Thermal Statistics

During the past 12 years there have been numerous papers on a relation between entropy and probability which is nonadditive and has a parameter q that depends on the nature of the thermodynamic system under consideration. For q=1 this relation corresponds to the Boltzmann-Gibbs entropy, but for other values of q it is claimed that it leads to a formalism that is consistent with the laws of thermodynamics. However, it is shown here that the joint entropy for systems having different values of q is not defined in this formalism, and consequently fundamental thermodynamic concepts such as temperature and heat exchange cannot be considered for such systems. Moreover, for q not equal 1 the probability distribution for weakly interacting systems does not factor into the product of the probability distribution for the separate systems, leading to spurious correlations and other unphysical consequences, e.g., nonextensive energy, that have been ignored in various applications given in the literature.