Extensive statistical mechanics based on nonadditive entropy Canonical ensemble.pdf

a r X i v : c o n d - m a t / 0 6 0 2 2 1 9 v 1 [ c o n d - m a t .s t a t - m e c h ] 8 F e b 2 0 0 6 Extensive statistical mechanics based on nonadditive entropy: Canonical ensemble A.S. Parvan Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, 141980 Dubna, Russia and Institute of Applied Physics, Moldova Academy of Sciences, MD-2028 Kishineu, Republic of Moldova The original canonical ensemble formalism for the nonextensive entropy thermostatistics is re- considered. It is shown that the unambiguous connection of the statistical mechanics with the equilibrium thermodynamics is provided if the entropic parameter 1/(q? 1) is an extensive variable of the state. Based on a particular example of the perfect gas, it is proved that the Tsallis thermo- statistics meets all the requirements of equilibrium thermodynamics in the thermodynamic limit. In particular, the entropy of the system is extensive and the temperature is intensive. However, for finite systems both the Tsallis and Boltzmann-Gibbs entropies are nonextensive. The equivalence of the canonical and microcanonical ensembles of Tsallis thermostatistics in the thermodynamic limit is established. The issue associated with physical interpretation of the entropic variable is discussed in detail. PACS numbers: 24.60. Ky, 25.70. Pq; 05.70.Jk I. INTRODUCTION The main purpose of this Letter is to establish a clear way to implement the equilibrium statistical mechanics based on the nonadditive entropy deferent from the usual Boltzmann-Gibbs statistical one. For the first time this concept was formulated by Tsallis in [1]. It is very well known that the conventional equilibrium statistical mechanics based on the Boltzmann-Gibbs entropy meets all the requirements of the equilibrium thermodynamics in the thermodynamic limit [2]. This is a necessary condition for self-consistent definition of any equilibrium statistical mechanics. In order to provide the connection of the statistica