Canonical ensemble in non-extensive statistical mechanics, q>1

2016 ◽  
Vol 458 ◽  
pp. 210-218 ◽  
Author(s):  
Julius Ruseckas
Keyword(s):  
Statistical Mechanics ◽  
Canonical Ensemble

Statistical mechanics of Fermi-Pasta-Ulam chains with the canonical ensemble

1997 ◽  
Vol 55 (3) ◽  
pp. 3727-3730
Author(s):  
Melik C. Demirel ◽  
Mehmet Sayar ◽  
Ali R. Atılgan
Keyword(s):  
Statistical Mechanics ◽  
Canonical Ensemble

scholarly journals Derivation of the entropic formula for the statistical mechanics of space plasmas

2018 ◽  
Vol 25 (1) ◽  
pp. 77-88 ◽  
Author(s):  
George Livadiotis
Keyword(s):  
Statistical Mechanics ◽  
Canonical Ensemble ◽  
Space Plasmas ◽  
Kappa Distribution ◽  
Physical Origin ◽  
Nonextensive Statistical Mechanics

Abstract. Kappa distributions describe velocities and energies of plasma populations in space plasmas. The statistical origin of these distributions is associated with the framework of nonextensive statistical mechanics. Indeed, the kappa distribution is derived by maximizing the q entropy of Tsallis, under the constraints of the canonical ensemble. However, the question remains as to what the physical origin of this entropic formulation is. This paper shows that the q entropy can be derived by adapting the additivity of energy and entropy.

scholarly journals Derivation of the entropic formula for the statistical mechanics of space plasmas

2017 ◽  
Author(s):  
George Livadiotis
Keyword(s):  
Statistical Mechanics ◽  
Canonical Ensemble ◽  
Space Plasmas ◽  
Kappa Distribution ◽  
Physical Origin

Abstract. Kappa distributions describe velocities and energies of plasma populations in space plasmas. The statistical origin of these distributions is the non-extensive statistical mechanics. Indeed, the kappa distribution is derived by maximizing the q-entropy of Tsallis under the constraints of canonical ensemble. However, there remains the question what is the physical origin of this entropic formulation. This paper shows that the q-entropy can be derived by adapting the additivity of energy and entropy.

Quantum Canonical Ensemble

2019 ◽  
pp. 297-321
Author(s):  
Robert H. Swendsen
Keyword(s):  
Statistical Mechanics ◽  
Canonical Ensemble ◽  
Quantum Statistical Mechanics ◽  
Harmonic Oscillators ◽  
Quantum Mechanical ◽  
The Third ◽  
Two Level Systems ◽  
Third Law ◽  
Quantum Statistical ◽  
The Relationship

This chapter introduces the quantum mechanical canonical ensemble, which is used for the majority of problems in quantum statistical mechanics. The ensemble is derived and analogies with the classical ensemble are presented. A useful expression for the quantum entropy is derived. The origin of the Third Law is explained. The relationship between fluctuations and derivatives found in classical statistical mechanics is shown to have counterparts in quantum statistical mechanics. The factorization of the partition function is re-introduced as the best trick in quantum statistical mechanics. Due to their importance in later chapters, basic calculations of the properties of two-level systems and simple harmonic oscillators are derived.

scholarly journals On the statistical mechanics of dilute and of perfect solutions

1932 ◽  
Vol 135 (826) ◽  
pp. 181-192 ◽  
Keyword(s):  
Statistical Mechanics ◽  
Mole Fraction ◽  
Simple Form ◽  
Infinite Dilution ◽  
Canonical Ensemble ◽  
Partition Functions ◽  
Dilute Solutions ◽  
Text Book ◽  
Thermodynamic Probability

1. Introduction and Definitions .—In a previous paper the author discussed the laws of dilute and of perfect solutions. It was pointed out that the laws of dilute solutions take different forms according to the concentration scale used, these forms becoming identical only at infinite dilution. Of these various sets of laws that corresponding to the mole-fraction scale of concentration has in certain respects simpler properties than the others and is more symmetrical between solvent and solute. In particular only in this form is it possible for the laws of dilute solutions to hold at all concentrations, in which case they become the laws of perfect solutions. It was shown how this set of laws of perfect solutions could be deduced by thermodynamic reasoning from certain assumptions about the additivity of energies and volumes on mixing, but these assumptions were not of a very simple form. Nor was any reason found why the laws of dilute solutions should take the particular form corresponding to the mole-fraction scale of concentration, except analogy with the laws of perfect solutions. In the present paper an attempt will be made to remedy this omission by considerations of statistical mechanics. The method used will be that of partition functions described in Fowler’s text-book. This method is more elegant than Gibbs’ method of the canonical ensemble, does not suffer from the logical inconsistencies of Boltzmann’s method of “thermodynamic probability,” and is more powerful than either of these.

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