Equilibrium statistical mechanics for incomplete nonextensive statistics
arXiv:1003.5630 · doi:10.1016/j.physleta.2010.12.022
Abstract
The incomplete nonextensive statistics in the canonical and microcanonical ensembles is explored in the general case and in a particular case for the ideal gas. By exact analytical results for the ideal gas it is shown that taking the thermodynamic limit, with being an extensive variable of state, the incomplete nonextensive statistics satisfies the requirements of equilibrium thermodynamics. The thermodynamical potential of the statistical ensemble is a homogeneous function of the first degree of the extensive variables of state. In this case, the incomplete nonextensive statistics is equivalent to the usual Tsallis statistics. If is an intensive variable of state, i.e. the entropic index is a universal constant, the requirements of the equilibrium thermodynamics are violated.
7 pages
References in corpus (16)
- Non Linear Kinetics underlying Generalized Statistics
- Incomplete statistics and nonextensive generalization of statistical mechanics
- Extensive Renyi Statistics from Non-Extensive Entropy
- Ideal gas in nonextensive optimal Lagrange multipliers formalism
- Temperature and pressure in nonextensive thermostatistics
- On the generalized entropy pseudoadditivity for complex systems
- Microcanonical Ensemble Extensive Thermodynamics of Tsallis Statistics
- Extensive statistical mechanics based on nonadditive entropy: Canonical ensemble
- Renyi statistics in equilibrium statistical mechanics
- Extensive form of equilibrium nonextensive statistics
- Non-extensive entropy from incomplete knowledge of Shannon entropy?
- Phase Transitions in Non-extensive Spin Systems
- Many-body q-exponential distribution prescribed by factorization hypothesis
- Possible canonical distributions for finite systems with nonadditive energy
- About "On certain incomplete statistics" by Lima et al
- Inherent correlations between thermodynamics and statistic physics in extensive and nonextensive systems