Results 1 - 10 of 51043
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[en] The Renyi statistics in the canonical and microcanonical ensembles is examined both in general and in particular for the ideal gas. In the microcanonical ensemble the Renyi statistics is equivalent to the Boltzmann-Gibbs statistics. By the exact analytical results for the ideal gas, it is shown that in the canonical ensemble, taking the thermodynamic limit, the Renyi statistics is also equivalent to 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 first degree of its extensive variables of state. We conclude that the Renyi statistics arrives at the same thermodynamical relations, as those stemming from the Boltzmann-Gibbs statistics in this limit.
[en] A deduction of generalized quantum entropies within the Tsallis and Kaniadakis frameworks is derived using a generalization of the ordinary multinomial coefficient. This generalization is based on the respective deformed multiplication and division. We show that the two above entropies are consistent with ones arbitrarily assumed at other contexts. -- Highlights: → Derivation of generalized quantum entropies. → Generalized combinatorial method. → Non-Gaussian quantum statistics.
[en] We show that the study of the microcanonical ensemble of free particles in a cubic box is identical to a problem encountered in the Theory of Numbers. The asymptotic formulation of this problem gives not only the usual formulae for Bose, Fermi and perfect gases, but also some idea of the importance of the approximations generaly used
[fr]Nous montrons comment l'etude d'un systeme de particules libres definissant un ensemble microcanonique se ramene a celle d'un probleme de la theorie analytique des nombres. Nous montrons ensuite comment la formulation asymptotique de ce probleme permet de retrouver les equations habituelles des gaz de Bose-Einstein et de Fermi-Dirac. Nous mettons egalement en evidence l'importance des approximations habituellement utilisees
[en] A theory for the nonequilibrium statistical mechanics of a liquid is presented. This theory consists of coupled evolution equations for the one-particle momentum distribution, and for the two-particle correlation function, and it possesses the same important properties as does Boltzmann's theory, namely the local conservation laws, the local h theorem, and the correct equilibrium solution
[en] We show that contrary to the commonly accepted view, Chapter IX of Gibbs's book  contains the prolegomena to a macroscopic statistical theory that is qualitatively different from his own microscopic statistical mechanics. The formulas obtained by Gibbs were the first results in the history of physics related to the theory of fluctuations in any macroparameters, including temperature. (from the history of physics)
[en] Generalized probability distributions for Maxwell-Boltzmann, Bose-Einstein and Fermi-Dirac statistics, with unequal source ('prior') probabilities qi for each level i, are obtained by combinatorial reasoning. For equiprobable degenerate sublevels, these reduce to those given by Brillouin in 1930, more commonly given as a statistical weight for each statistic. These distributions and corresponding cross-entropy (divergence) functions are shown to be special cases of the Polya urn model, involving neither independent nor identically distributed ('ninid') sampling. The most probable Polya distribution is shown to contain the Acharya-Swamy intermediate statistic
[en] A characterization of states, over quasi-local algebras, which satisfy a strong cluster property is derived. The discussion is applicable to classical systems and quantum systems with Bose or Fermi statistics. (orig.)
[de]Eine Charakterisierung von Zustaenden wird ueber quasi-lokale Algebras abgeleitet, die eine starke Clusterbedingung erfuellen. Die Diskussion ist auf klassische Systeme und Quantensysteme mit Bose- oder Fermistatistiken anwendbar. (orig./AK)
[en] The aim of this tutorial is to present the basic mathematical techniques required for an accurate description of cold trapped atoms, both Bose and Fermi. The term cold implies that considered temperatures are low, such that quantum theory is necessary, even if temperatures are finite. The term atoms means that the considered particles are structureless, being defined by their masses and mutual interactions. Atoms are trapped in the sense that they form a finite quantum system, though their number can be very large, allowing for the use of the methods of statistical mechanics. This tutorial is the first of several, giving general mathematical techniques for both types of particle statistics. The following tutorials will be devoted separately to Bose atoms and Fermi atoms. Carefully explaining basic techniques is important in order to avoid the numerous misconceptions which propagate in the literature. (tutorial)
[en] A measure of complexity for sequentially created symbolic patterns is introduced. The underlying grammatical rules are systematically detected in terms of variable-length prefix-free codewords and arranged on a 'logic' tree. Predictions on the scaling structure of the system are then formulated and compared with the observation. The discrepancy between the two, evaluated through a generalisation of the information gain, characterises the complexity of the system, relative to the unfolding scheme. (author) 1 fig., 20 refs