The van der Waals limit for classical systems. I. A variational principle |
| |
Authors: | D J Gates O Penrose |
| |
Institution: | (1) Mathematics Department, Imperial College, S.W.7 London;(2) The Open University Walton Hall, Bletchley, Bucks, Great Britain |
| |
Abstract: | We consider the thermodynamic pressurep(, ) of a classical system of particles with the two-body interaction potentialq(r)+
v
K(r), where is the number of space dimensions, is a positive parameter, and is the chemical potential. The temperature is not shown in the notation. We prove rigorously, for hard-core potentialsq(r) and for a very general class of functionsK(s), that the limit 0 of the pressurep(, ) exists and is given by where the limit and the supremum can be interchanged. Here is a certain class of nonnegative, Riemann integrable functions,D is a cube of volume |D|, anda
0() is the free energy density of a system withK=0 and density . A similar result is proved for the free energy. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|