Basic Principles

Carlo Cercignani
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Carlo Cercignani: Politecnico di Milano

Chapter Chapter I in Mathematical Methods in Kinetic Theory, 1990, pp 1-39 from Springer

Abstract: Abstract The kinetic theory of gases is a part of statistical mechanics, i.e., of the statistical theory of the dynamics of mechanical systems formed by a great number of particles, such as the number of molecules contained in a lump of matter of macroscopic dimensions. The aim of statistical mechanics is to explain the macroscopic behavior of matter in terms of the mechanical behavior of the constituent molecules, i.e., in terms of motions and interactions of a large number of particles. We shall assume that classical mechanics can be applied, and, therefore, the molecules are subject to Newton’s second law where x i is the position vector of the ith particle (i = 1,…, N) and ξ i its velocity vector ; both x i and ξ i are functions of the time variable t, and the dots denote, as usual, differentiation with respect to t. Here X i is the force acting upon the ith particle divided by the mass of the particle. Such a force will in general be the sum of an external force (e.g., gravity or centrifugal forces) and the force describing the action of the other particles of the system on the ith particle. The expression of such forces must be given as part of the description of the mechanical system.

Keywords: Phase Space; Boltzmann Equation; Thermal Equilibrium; Liouville Equation; Collision Operator (search for similar items in EconPapers)
Date: 1990
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DOI: 10.1007/978-1-4899-7291-0_1

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