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By G.H. A. Cole
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Extra resources for An Introduction to the Statistical Theory of Classical Simple Dense Fluids
10) for all particles i and j of the group of A particles. 6) when the particle relative orientation is either irrelevant (spherical particles) or has been integrated away. 2. THE CANONICAL FORM The phase and configuration distribution functions set down so far apply to any steady situation whether it refers to equilibrium or not. To make them apply specifically to equilibrium conditions it is necessary to add a supplementary statement that non-equilibrium is explicitly excluded, and this is achieved by assigning a special form to the 7V-th order phase distribution f<*>.
R = d76 - äi7' (2 10a) - where/ = 1, 2, 3, . . N. 1). 10) can be regarded as an alternative statement of Newton's laws of motion. From Newton's second law pj is equal to the vector force acting on the particle, written F·, so that F3- = - ^ - . 3). 10) is called the phase. The time evolution of the system of N particles contained in volume V is then to be represented by a specification of the phase as function of the time. Such a representation can conveniently assume a geometrical form. The geometrical plotting can refer either to each particle taken separately from the remainder, or to the total system of particles treated collectively.
Will be written W(rl9 r 2 , r 3 , . . r^). If the interaction between any two particles is not directly influenced by the presence of a third particle, the total potential Ψ can be replaced by the sum of the separate pair interactions. For this case2, Ψ(τΐ9 r 2 , r3, .. 1) where ψ is the interaction potential for the representative pair of particles i and j : ip is usually called the pair potential. 1) is to N(N-1) include all the contributions from the —L— pairs of particles that can be constructed from the N particles of the system.
An Introduction to the Statistical Theory of Classical Simple Dense Fluids by G.H. A. Cole