Renyi statistics in equilibrium statistical mechanics
arXiv:0910.3062 · doi:10.1016/j.physleta.2010.03.007
Abstract
The Renyi statistics in the canonical and microcanonical ensembles is examined in the general case and in particular for the ideal gas. In the microcanonical ensemble the Renyi statistics is equivalent with the Boltzmann-Gibbs statistics. By the exact analytical results for the ideal gas, it is shown that in the canonical ensemble in the thermodynamic limit the Renyi statistics is also equivalent with the Boltzmann-Gibbs statistics. Furthermore it satisfies the requirements of the equilibrium thermodynamics, i.e. the thermodynamical potential of the statistical ensemble is a homogeneous function of degree 1 of its extensive variables of state. We conclude that the Renyi statistics duplicates the thermodynamical relations stemming from the Boltzmann-Gibbs statistics in the thermodynamical limit.
13 pages
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- Nonequilibrium statistical operator method in the Renyi statistics
- Thermodynamics of the independent harmonic oscillators with different frequencies in the Tsallis statistics
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- Equilibrium statistical mechanics for incomplete nonextensive statistics
- Critique of multinomial coefficients method for evaluating Tsallis and Renyi entropies
- Thermodynamic quantities of independent harmonic oscillators in microcanonical and canonical ensembles in the Tsallis statistics
- Thermodynamic relations and fluctuations in the Tsallis statistics
- Ising model in the Rényi statistics: the finite size effects
- The statistics of mesoscopic systems and the physical interpretation of extensive and non-extensive entropies