By G.H. A. Cole
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Extra resources for An Introduction to the Statistical Theory of Classical Simple Dense Fluids
This relation involves a knowledge of the distribution functions appropriate to a fluid under specific macroscopic conditions: the determination of the appropriate distribution functions for a specific fluid state is, therefore, one of the central problems of microscopic statistical physics. 36 STATISTICAL THEORY OF CLASSICAL FLUIDS If the particle interaction forces are primarily those between small groupings of particles, for instance between pairs of particles, a knowledge of the full phase distribution / ( i V ) may not always be necessary in the calculation of phase averages appropriate to certain physical situations.
It will be found that for equilibrium conditions / (iV) has the canonical form of Gibbs; for non-equilibrium the appropriate distribution is to be determined from equations that are still under construction. 10) are of the first order, so that a knowledge of the phase at any time t is sufficient to determine the phase at any later (or earlier) time. 11b) that the y-phase distribution behaves as an incompressible fluid. e. 22) can be rewritten in the form: —ΒΓ- A \Έ>'-5ΪΓΓ& (« ~*r)· ( } This is an alternative statement of Liouville's theorem and is called the Liouville equation.
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<*>.