Possible divergences in Tsallis' thermostatistics

Abstract

Trying to compute the nonextensive q-partition function for the Harmonic Oscillator in more than two dimensions, one encounters that it diverges, which poses a serious threat to Tsallis’ thermostatistics. Appeal to the so called q-Laplace Transform, where the q-exponential function plays the role of the ordinary exponential, is seen to save the day.