Extensive statistical mechanics based on nonadditive entropy: Canonical ensemble
arXiv:cond-mat/0602219 · doi:10.1016/j.physleta.2006.07.052
Abstract
The original canonical ensemble formalism for the nonextensive entropy thermostatistics is reconsidered. It is shown that the unambiguous connection of the statistical mechanics with the equilibrium thermodynamics is provided if the entropic parameter is an extensive variable of the state. Based on a particular example of the perfect gas, it is proved that the Tsallis thermostatistics 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.
11 pages, 1 figure
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- Finite size effects in the thermodynamics of a free neutral scalar field
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- Ising model in the Rényi statistics: the finite size effects