scholarly journals Consistent Order Approximations in Extended Thermodynamics of Polyatomic Gases

2021 ◽  
Vol 1 (2) ◽  
pp. 12-21
Author(s):  
Sebastiano Pennisi
Keyword(s):  
Maximum Entropy ◽  
Arbitrary Number ◽  
Maximum Entropy Principle ◽  
Extended Thermodynamics ◽  
The Other ◽  
Balance Equations ◽  
Polyatomic Gases ◽  
New Model ◽  
Independent Variables ◽  
Entropy Principle

In this article the known models are considered for relativistic polyatomic gases with an arbitrary number of moments, in the framework of Extended Thermodynamics. These models have the downside of being hyperbolic only in a narrow domain around equilibrium, called "hyperbolicity zone". Here it is shown how to overcome this drawback by presenting a new model which satisfies the hyperbolicity requirement for every value of the independent variables and without restrictions. The basic idea behind this new model is that hyperbolicity is limited in previous models by the approximations made there. It is here shown that hyperbolicity isn't limited also for an approximated model if terms of the same order are consistently considered, in a new way never used before in literature. To design and complete this new model, well accepted principles are used such as the "Entropy Principle" and the "Maximum Entropy Principle". Finally, new trends are analized and these considerations may require a modification of the results published so far; as a bonus, more manageable balance equations are obtained. This allows to obtain more stringent results than those so far known. For example, we will have a single quantity (the energy e) expressed by an integral and all the other constitutive functions will be expressed in terms of it and its derivatives with respect to temperature. Another useful consequence is its easier applicability to the case of diatomic and ultrarelativistic gases which are useful, at least for testing the model in simple cases.

scholarly journals Molecular Extended Thermodynamics of Rarefied Polyatomic Gases with a New Hierarchy of Moments

Fluids ◽  
2021 ◽  
Vol 6 (2) ◽  
pp. 62
Author(s):  
Takashi Arima ◽  
Tommaso Ruggeri
Keyword(s):  
Degrees Of Freedom ◽  
Maximum Entropy Principle ◽  
Extended Thermodynamics ◽  
Moment Equations ◽  
Field Equations ◽  
Polyatomic Gases ◽  
Moment System ◽  
Rarefied Polyatomic Gases ◽  
Entropy Principle ◽  
Internal Degrees Of Freedom

The aim of this paper is to construct the molecular extended thermodynamics for classical rarefied polyatomic gases with a new hierarchy, which is absent in the previous procedures of moment equations. The new hierarchy is deduced recently from the classical limit of the relativistic theory of moments associated with the Boltzmann–Chernikov equation. The field equations for 15 moments of the distribution function, in which the internal degrees of freedom of a molecule are taken into account, are closed with the maximum entropy principle. It is shown that the theory contains, as a principal subsystem, the previously polyatomic 14 fields theory, and in the monatomic limit, in which the dynamical pressure vanishes, the differential system converges, instead of to the Grad 13-moment system, to the Kremer 14-moment system.

scholarly journals Derivation of some new distributions in statistical mechanics using maximum entropy approach

2014 ◽  
Vol 24 (1) ◽  
pp. 145-155 ◽  
Author(s):  
Amritansu Ray ◽  
S.K. Majumder
Keyword(s):  
Statistical Mechanics ◽  
Maximum Entropy ◽  
Maximum Entropy Principle ◽  
The Other ◽  
Central Idea ◽  
Entropy Principle ◽  
Bose Einstein ◽  
The Way

The maximum entropy principle has been earlier used to derive the Bose Einstein(B.E.), Fermi Dirac(F.D.) & Intermediate Statistics(I.S.) distribution of statistical mechanics. The central idea of these distributions is to predict the distribution of the microstates, which are the particle of the system, on the basis of the knowledge of some macroscopic data. The latter information is specified in the form of some simple moment constraints. One distribution differs from the other in the way in which the constraints are specified. In the present paper, we have derived some new distributions similar to B.E., F.D. distributions of statistical mechanics by using maximum entropy principle. Some proofs of B.E. & F.D. distributions are shown, and at the end some new results are discussed.

scholarly journals What Is the Maximum Entropy Principle? Comments on “Statistical Theory on the Functional Form of Cloud Particle Size Distributions”

2019 ◽  
Vol 76 (12) ◽  
pp. 3955-3960 ◽  
Author(s):  
Jun-Ichi Yano
Keyword(s):  
Maximum Entropy ◽  
Relative Entropy ◽  
Functional Form ◽  
Maximum Entropy Principle ◽  
The Other ◽  
Standard Entropy ◽  
Size Distributions ◽  
Particle Size Distributions ◽  
Cloud Particle ◽  
Entropy Principle

Abstract The basic idea of the maximum entropy principle is presented in a succinct, self-contained manner. The presentation points out some misunderstandings on this principle by Wu and McFarquhar. Namely, the principle does not suffer from the problem of a lack of invariance by change of the dependent variable; thus, it does not lead to a need to introduce the relative entropy as suggested by Wu and McFarquhar. The principle is valid only with a proper choice of a dependent variable, called a restriction variable, for a distribution. Although different results may be obtained with the other variables obtained by transforming the restriction variable, these results are simply meaningless. A relative entropy may be used instead of a standard entropy. However, the former does not lead to any new results unobtainable by the latter.

Maximum-entropy closure for a Galerkin model of an incompressible periodic wake

2012 ◽  
Vol 700 ◽  
pp. 187-213 ◽  
Author(s):  
Bernd R. Noack ◽  
Robert K. Niven
Keyword(s):  
Maximum Entropy ◽  
Energy Levels ◽  
Maximum Entropy Principle ◽  
Mean Amplitude ◽  
Navier Stokes ◽  
Cylinder Wake ◽  
Balance Equations ◽  
Side Constraints ◽  
Entropy Principle ◽  
Good Agreement

AbstractA statistical closure is proposed for a Galerkin model of an incompressible periodic cylinder wake. This closure employs Jaynes’ maximum entropy principle to infer the probability distribution for mode amplitudes using exact statistical balance equations as side constraints. The analysis predicts mean amplitude values and modal energy levels in good agreement with direct Navier–Stokes simulation. In addition, it provides an analytical equation for the modal energy distribution.

scholarly journals Moment Equations with Maximum Entropy Closure for Carrier Transport in Semiconductor Devices: Validation in Bulk Silicon

VLSI Design ◽  
2000 ◽  
Vol 10 (4) ◽  
pp. 335-354 ◽  
Author(s):  
A. M. Anile ◽  
O. Muscato ◽  
V. Romano
Keyword(s):  
Maximum Entropy ◽  
Moment Method ◽  
Carrier Transport ◽  
Maximum Entropy Principle ◽  
Bulk Silicon ◽  
Moment Equations ◽  
Balance Equations ◽  
Entropy Principle ◽  
Closure Relations ◽  
The Moment

Balance equations based on the moment method for the transport of electrons in silicon semiconductors are presented. The energy band is assumed to be described by the Kane dispersion relation. The closure relations have been obtained by employing the maximum entropy principle.The validity of the constitutive equations for fluxes and production terms of the balance equations has been checked with a comparison to detailed Monte Carlo simulations in the case of bulk silicon.

scholarly journals A Numberable Set of Exact Solutions for the Macroscopic Approach to Extended Thermodynamics of Polyatomic Gases with Many Moments

2016 ◽  
Vol 2016 ◽  
pp. 1-8 ◽  
Author(s):  
Maria Cristina Carrisi ◽  
Rita Enoh Tchame ◽  
Marcel Obounou ◽  
Sebastiano Pennisi
Keyword(s):  
Exact Solutions ◽  
Fixed Number ◽  
Extended Thermodynamics ◽  
Relativity Principle ◽  
Polyatomic Gases ◽  
New Model ◽  
Galilean Relativity ◽  
Entropy Principle ◽  
Macroscopic Approach ◽  
Particular Solution

A new model for Polyatomic Gases with an arbitrary but fixed number of moments has been recently proposed and investigated in the framework of Extended Thermodynamics; the arbitrariness of the number of moments is linked to a numberNand the resulting model is called anN-Model. This model has been elaborated in order to take into account the entropy principle, the Galilean relativity principle, and some symmetry conditions. It has been proved that the solution for all these conditions exists, but it has not been written explicitly because hard notation is necessary; it has only been shown how the theory is self-generating in the sense that if we know the closure of theN-Model, then we will be able to find that of(N+1)-Model. Up to now only a single particular solution has been found in this regard. Instead of this, we find here a numberable set of exact solutions which hold for every fixed numberN.

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