Statistical properties of the cluster dynamicsof the systems of statistical mechanics

摘要

L. Boltzmann was the first who tried to explain the laws of thermodynamics and kineticsas corollaries of dynamics of large systems of interacting particles (see his classicalbook [1]). In particular, Boltzmann derived the classical Boltzmann kinetic equationbased on his Stobzahlansatz that gave the first "dynamical" explanation of irreversibility.The StoBzahlansatz can be applied to any system of statistical mechanics which canbe considered as a small perturbation of an ideal gas and undergoes the so-calledBoltzmann-Grad limit transition (see [3]) when the length of the free path is of theorder of the size of the whole system. O. Lanford (see [3]) gave the first mathematicalproof of the local existence theorem of solutions of the Boltzmann equation where heshowed convergence of correlation functions to solutions of the Boltzmann equation.