scholarly journals Maximum entropy principle for rarefied polyatomic gases

2013 ◽  
Vol 392 (6) ◽  
pp. 1302-1317 ◽  
Author(s):  
Milana Pavić ◽  
Tommaso Ruggeri ◽  
Srboljub Simić
Keyword(s):  
Maximum Entropy ◽  
Maximum Entropy Principle ◽  
Polyatomic Gases ◽  
Rarefied Polyatomic Gases ◽  
Entropy Principle

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 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.

An entropy concentration theorem: applications in artificial intelligence and descriptive statistics

1990 ◽  
Vol 27 (2) ◽  
pp. 303-313 ◽  
Author(s):  
Claudine Robert
Keyword(s):  
Artificial Intelligence ◽  
Maximum Entropy ◽  
Large Deviation ◽  
Maximum Entropy Principle ◽  
Statistical Modelling ◽  
Linear Constraints ◽  
Descriptive Statistics ◽  
Entropy Principle ◽  
Maximum Entropy Distribution ◽  
Mathematical Justification

The maximum entropy principle is used to model uncertainty by a maximum entropy distribution, subject to some appropriate linear constraints. We give an entropy concentration theorem (whose demonstration is based on large deviation techniques) which is a mathematical justification of this statistical modelling principle. Then we indicate how it can be used in artificial intelligence, and how relevant prior knowledge is provided by some classical descriptive statistical methods. It appears furthermore that the maximum entropy principle yields to a natural binding between descriptive methods and some statistical structures.

SINE ENTROPY FOR UNCERTAIN VARIABLES

2013 ◽  
Vol 21 (05) ◽  
pp. 743-753 ◽  
Author(s):  
KAI YAO ◽  
JINWU GAO ◽  
WEI DAI
Keyword(s):  
Maximum Entropy ◽  
Uncertainty Theory ◽  
Maximum Entropy Principle ◽  
Expected Value ◽  
Uncertain Variables ◽  
Entropy Principle

Entropy is a measure of the uncertainty associated with a variable whose value cannot be exactly predicated. In uncertainty theory, it has been quantified so far by logarithmic entropy. However, logarithmic entropy sometimes fails to measure the uncertainty. This paper will propose another type of entropy named sine entropy as a supplement, and explore its properties. After that, the maximum entropy principle will be introduced, and the arc-cosine distributed variables will be proved to have the maximum sine entropy with given expected value and variance.

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