Thermodynamic limit of a classical gas in nonextensive statistical mechanics: Negative specific heat and polytropism

Within the framework of canonical ensemble theory in Tsallis' nonextensive statistical mechanics with the normalized q-expectation values, the classical gas model is studied and its exact solution is obtained. It is shown that the negative specific heat, which appears in astrophysical problems, can be realized in the range of the nonextensivity parameter and in the thermodynamic limit the pressure and the particle number density obey the polytrope-type relation. It is also shown that the Boltzmann-Gibbs limit (q-->1-)and the thermodynamic limit do not commute with each other. (C) 1999 Elsevier Science B.V. All rights reserved.