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

@article{50310,
   author = {Cremaschini, Claudio and Tessarotto, Massimo},
   article_location = {DE - Spolková republika Německo},
   article_number = {7},
   doi = {http://dx.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://dx.doi.org/10.1140/epjp/i2014-14157-4.