The Master kinetic equation for the statistical treatment of
the Boltzmann-Sinai classical dynamical system

J 2014

The Master kinetic equation for the statistical treatment of the Boltzmann-Sinai classical dynamical system

CREMASCHINI, Claudio and Massimo TESSAROTTO

Basic information

Original name

The Master kinetic equation for the statistical treatment of the Boltzmann-Sinai classical dynamical system

Authors

CREMASCHINI, Claudio and Massimo TESSAROTTO

Edition

European Physical Journal Plus, DE - Spolková republika Německo, 2014, 2190-5444

Other information

Language

English

Type of outcome

Article in a journal

Field of Study

10300 1.3 Physical sciences

Confidentiality degree

is not subject to a state or trade secret

References:

URL

Impact factor

Impact factor: 1.377

Organization unit

Institute of physics in Opava

DOI

https://doi.org/10.1140/epjp/i2014-14157-4

UT WoS

000339959500001

Keywords in English

Enskog kinetic equation; Boltzmann-Sinai system

Abstract

In the original language

In this investigation, exact particular realizations are sought for the microscopic statistical description which is associated with the classical dynamical system (CDS) formed by N identical smooth hard spheres subject to elastic collisions (S_N-CDS). The problem is posed in the framework of the ab initio statistical description of S_N-CDS recently developed. It is shown that the Liouville equation associated with S_N-CDS admits an exact particular solution for the N-body probability density function (PDF). This is factorized in terms of the i-th particle 1-body PDF (for all i = 1, N) via suitable weighting factors, which are denoted here as particle occupation coefficients. The latter are found to depend functionally only on the 1-body PDFs which areassociated with each of the remaining particles belonging to S_N-CDS. Furthermore, the 1-body PDF is proved to obey a well-defined statistical equation, referred to here as Master kinetic equation. This is an exact kinetic equation which

Cite

CREMASCHINI, Claudio and Massimo TESSAROTTO. The Master kinetic equation for the statistical treatment of the Boltzmann-Sinai classical dynamical system. European Physical Journal Plus. DE - Spolková republika Německo, 2014, vol. 129, No 7, 33 pp. ISSN 2190-5444. Available from: https://doi.org/10.1140/epjp/i2014-14157-4.

@article{50310,
   author = {Cremaschini, Claudio and Tessarotto, Massimo},
   article_location = {DE - Spolková republika Německo},
   article_number = {7},
   doi = {https://doi.org/10.1140/epjp/i2014-14157-4},
   keywords = {Enskog kinetic equation; Boltzmann-Sinai system},
   language = {eng},
   issn = {2190-5444},
   journal = {European Physical Journal Plus},
   title = {The Master kinetic equation for the statistical treatment of the Boltzmann-Sinai classical dynamical system},
   url = {https://link.springer.com/article/10.1140/epjp/i2014-14157-4},
   volume = {129},
   year = {2014}
}

TY  - JOUR
ID  - 50310
AU  - Cremaschini, Claudio - Tessarotto, Massimo
PY  - 2014
TI  - The Master kinetic equation for the statistical treatment of the Boltzmann-Sinai classical dynamical system
JF  - European Physical Journal Plus
VL  - 129
IS  - 7
SN  - 21905444
KW  - Enskog kinetic equation
KW  - Boltzmann-Sinai system
UR  - https://link.springer.com/article/10.1140/epjp/i2014-14157-4
N2  - In this investigation, exact particular realizations are sought for the microscopic statistical description which is associated with the classical dynamical system (CDS) formed by N identical smooth hard spheres subject to elastic collisions (S_N-CDS). The problem is posed in the framework of the ab initio statistical description of S_N-CDS recently developed. It is shown that the Liouville equation associated with S_N-CDS admits an exact particular solution for the N-body probability density function (PDF). This is factorized in terms of the i-th particle 1-body PDF (for all i = 1, N) via suitable weighting factors, which are denoted here as particle occupation coefficients. The latter are found to depend functionally only on the 1-body PDFs which areassociated with each of the remaining particles belonging to S_N-CDS. Furthermore, the 1-body PDF is proved to obey a well-defined statistical equation, referred to here as Master kinetic equation. This is an exact kinetic equation which
ER  -

CREMASCHINI, Claudio and Massimo TESSAROTTO. The Master kinetic equation for the statistical treatment of the Boltzmann-Sinai classical dynamical system. \textit{European Physical Journal Plus}. DE - Spolková republika Německo, 2014, vol.~129, No~7, 33 pp. ISSN~2190-5444. Available from: https://doi.org/10.1140/epjp/i2014-14157-4.

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