<i>Statistical Mechanics</i>

Huang, Kerson; Holbrow, Charles H.

doi:10.1063/1.3047170

Cited by 577 publications

(161 citation statements)

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“…This function is different from the one calculated by the Maxwell-Boltzmann function [10], it has the explicit dependence on q through the term q Aq 1 f (0) , which is unity in the extensive limit. The quantity < U i U j > q , in this order of approximation, is given by:…”

Section: The First Order Approximationmentioning

confidence: 99%

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Transport theory in the context of the normalized generalized statistics

Potiguar

Costa

2002

Physica A: Statistical Mechanics and its Applications

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In this work assuming valid the equipartition theorem and using the normalized q-expectation value, we obtain, until first order approximation, the hydrodynamics equation for the generalized statistics. This equations are different from those obtained in the context of the Boltzmann-Gibbs statistics. This difference is that now appears two transport coefficient that depend on the q-value. PACS number(s): 05.20.Jj, 05.20.Gg

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Section: The First Order Approximationmentioning

confidence: 99%

“…We'll follow reference [10] and assume the energy equipartition theorem to be valid [7]. We are studying an ideal gas in the 6-dimensional phase space.…”

Section: Normalized Hydrodynamic Equationsmentioning

confidence: 99%

Transport theory in the context of the normalized generalized statistics

Potiguar

Costa

2002

Physica A: Statistical Mechanics and its Applications

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“…. is the occupation number of states (cf., e.g., Kittel and Kroemer, 1980;Huang, 1987), and p = (p), µ are the respective energy as function of momentum p and chemical potential, the latter being a function of density. β is the inverse kinetic temperature, with the latter taken in energy units.…”

Section: Formulationmentioning

confidence: 99%

“…This makes its use as a physical distribution more difficult and requires use of approximation methods to eliminate µ. This must be done by standard procedures referring to the density as a known quantity (cf., e.g., Huang, 1987). In space-plasma applications the kappa distribution is used as a probability, and it is assumed that µ = 0 which implies that the particles under consideration behave like massless Bosons.…”

Section: Classical Limitmentioning

confidence: 99%

Generalised partition functions: inferences on phase space distributions

Treumann

Baumjohann

2016

Ann. Geophys.

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Abstract. It is demonstrated that the statistical mechanical partition function can be used to construct various different forms of phase space distributions. This indicates that its structure is not restricted to the Gibbs-Boltzmann factor prescription which is based on counting statistics. With the widely used replacement of the Boltzmann factor by a generalised Lorentzian (also known as the q-deformed exponential function, where κ = 1/|q − 1|, with κ, q ∈ R) both the kappa-Bose and kappa-Fermi partition functions are obtained in quite a straightforward way, from which the conventional Bose and Fermi distributions follow for κ → ∞. For κ = ∞ these are subject to the restrictions that they can be used only at temperatures far from zero. They thus, as shown earlier, have little value for quantum physics. This is reasonable, because physical κ systems imply strong correlations which are absent at zero temperature where apart from stochastics all dynamical interactions are frozen. In the classical large temperature limit one obtains physically reasonable κ distributions which depend on energy respectively momentum as well as on chemical potential. Looking for other functional dependencies, we examine Bessel functions whether they can be used for obtaining valid distributions. Again and for the same reason, no Fermi and Bose distributions exist in the low temperature limit. However, a classical Bessel-Boltzmann distribution can be constructed which is a Bessel-modified Lorentzian distribution. Whether it makes any physical sense remains an open question. This is not investigated here. The choice of Bessel functions is motivated solely by their convergence properties and not by reference to any physical demands. This result suggests that the Gibbs-Boltzmann partition function is fundamental not only to Gibbs-Boltzmann but also to a large class of generalised Lorentzian distributions as well as to the corresponding nonextensive statistical mechanics.

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“…In a second order phase transition, the specific heat and the susceptibility, which are the second derivatives of the free energy (with respect to temperature and magnetic field, respectively) are discontinuous at the transition line [23].…”

Section: Theoretical Frameworkmentioning

confidence: 99%

Thermodynamics of third order phase transition: A solution to the Euler–Lagrange equations

Ekuma

Asomba

Okoye

2010

Physica B: Condensed Matter

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Abstract:The thermodynamics expected of systems undergoing third order phase transition has been investigated by identifying the orders through the analytic continuation of the functional of the free energy, using Ehrenfest thermodynamic theory. We developed the Euler -Lagrange equations for the order parameter and the vector potential and solved them for the first time using well -known mathematical formulations.

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Statistical Mechanics

Cited by 577 publications

References 0 publications

Transport theory in the context of the normalized generalized statistics

Transport theory in the context of the normalized generalized statistics

Generalised partition functions: inferences on phase space distributions

Thermodynamics of third order phase transition: A solution to the Euler–Lagrange equations

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