Phase density method: a microscopic description of the gas of neutral particles.
This paper is devoted to the construction of local microscopic equations describing the evolution of the gas that is treated as a system of a finite number N of point particles placed in a given fixed volume of space. It is assumed that, given an arbitrary motion of the particles, the state of each of them is characterized by a set s (1<or=s<infinity) of dynamic nonzero variables. Such a set represents a point in some 3s-dimensional phase space. The notion of the s-th order phase density is introduced, and it is shown that the hierarchy of densities satisfies an infinite system of coupled integrodifferential equations. The structure of the equations suggests the conditions, under which they can be transformed to a closed system of p differential equations: a functional relation between the (p+1)th and the other p dynamic variables must be specified. For the gas of neutral particles, such a relation is found from ordinary equations of motion of particles (p=2). However, the acceleration of an individual particle turns out to be a function not only of its coordinates and velocity but also of the coordinates and velocity of the other (N-1) particles of the system having the role of the field sources. The presence of an additional coupling leads to the "splitting" of the second of the two remaining evolution equations into a closed system of N equations for so-called multiparticle phase densities. The physical meaning of these equations and their possible implications for the kinetic theory of gases are discussed. It is stressed that a similar system of microscopic equations can be constructed for any microscopic quantities of the system of particles under consideration.
Yevstafiev
V V
VV
Institute of Solar-Terrestrial Physics SD RAS, Irkutsk 664033, Russia.