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@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.
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