Theory of collisional invariants for the Master kinetic equation

@article{50360,
   author = {Cremaschini, Claudio and Tessarotto, Massimo},
   article_location = {NL - Nizozemsko},
   article_number = {18-19},
   doi = {http://dx.doi.org/10.1016/j.physleta.2015.02.024},
   keywords = {classical statistical mechanics; hard-sphere system; collisional invariants; Boltzmann equation; statistical entropy density},
   language = {eng},
   issn = {0375-9601},
   journal = {Physics Letters A},
   title = {Theory of collisional invariants for the Master kinetic equation},
   url = {https://www.sciencedirect.com/science/article/abs/pii/S0375960115001954},
   volume = {379},
   year = {2015}
}

TY  - JOUR
ID  - 50360
AU  - Cremaschini, Claudio - Tessarotto, Massimo
PY  - 2015
TI  - Theory of collisional invariants for the Master kinetic equation
JF  - Physics Letters A
VL  - 379
IS  - 18-19
SP  - 1206-1212
EP  - 1206-1212
SN  - 03759601
KW  - classical statistical mechanics
KW  - hard-sphere system
KW  - collisional invariants
KW  - Boltzmann equation
KW  - statistical entropy density
UR  - https://www.sciencedirect.com/science/article/abs/pii/S0375960115001954
N2  - The paper investigates the integral conservation properties of the Master kinetic equation, which provides an exact kinetic statistical description for the Boltzmann-Sinai classical dynamical system. It is proved that, besides the customary Boltzmann collisional invariants, this equation admits also a class of generalized collisional invariants (GCI). The result applies only when the number N and the diameter sigma of hard-spheres are finite. This includes the case of dilute gases for which suitable asymptotic ordering conditions hold. However, when the Boltzmann-Grad limit is performed on the Master kinetic equation, it is shown that the existence of GCI is not permitted anymore.
ER  - 

CREMASCHINI, Claudio a Massimo TESSAROTTO. Theory of collisional invariants for the Master kinetic equation. \textit{Physics Letters A}. NL - Nizozemsko, 2015, roč.~379, 18-19, s.~1206-1212. ISSN~0375-9601. Dostupné z: https://dx.doi.org/10.1016/j.physleta.2015.02.024.