Molecular Dynamics (and, to a lesser extent Monte Carlo methods) made it easy to find equations of state and transport coefficients without the need for elaborate analyses. Some of the interesting papers are Alder and Wainwright's contribution to a symposium "Transport Processes in Statistical Mechanics", held in Brussels in 1956, Vineyard's description of radiation-damage studies of metals [(Physical Review 120 (1960)], Levesque, Verlet, and Kürkijarvi's study [Physical Review A 7 (1973)] of the equilibrium and transport properties for Lennard-Jones 12-6 pair potential, and the spate of papers detailing the perturbation theory approach to fluid equations of state. Solid-phase elastic constants were studied too [Squire, Holt, and Hoover, Physica 42, 388 and 44, 437 (1969)]. A low-cost approach to thermodynamics involving free volumes and the "cell model" leads to interesting exact relationships. See the paper by me and my son on this subject [Journal of Chemical Physics 70, 1837 (1968)], written while on sabbatical at the Australian National University. The voluminous literature in this area even includes a case of bogus data [see the discussion in Holian, Posch and Hoover, Physical Review E 47, 3852 (1993)], which is otherwise quite rare in classical computer simulations.

*The Melting
Transition*

When I first came to Livermore, before hard-sphere perturbation theory came into common use, the melting and freezing transitions were challenging conceptual problems. Francis Ree and I used Kirkwood's single-occupancy idea to calculate the Helmholtz free energy and communal entropy for hard-disk and hard-sphere solids. The calculation is described in our 1968 paper, Melting Transition and Communal Entropy for Hard Spheres. The communal-entropy calculations allowed us to locate the transition pressure at which the disks and spheres melted (and froze). The theoretical interpretation of such results was (and still is) muddled by the existence of approximate "theories" (Born's idea that melting occurs when the solid shear modulus vanishes and the Kosterlitz-Thouless idea, attributed by Farid Abraham to Dick Feynman, that melting occurs when dislocations form spontaneously). Abraham pointed out, a bit immodestly, that such one-phase theories always overestimate the melting temperature and underestimate the density. Otherwise put, the contribution of defects such as vacancies and dislocations to solid-phase properties is nearly negligible so far as its effect on melting is concerned. It is hard to understand the current reluctance to accept the first-order melting of disks, which appears to have been better understood in the 1970s than it is today!

*Selected
Publications:*

*
Computational Statistical Mechanics (published in 1991 by Elsevier) [as a
service to potential "gentle readers" of this out-of-print book a pdf file
is provided here.]*

*
Molecular Dynamics (published in 1985 by Springer Verlag, but out-of-print
and provided here as another service to the gentle readers.)*

*
Melting and the Virial Series for Hard Disks and Spheres [Journal of Chemical
Physics 49,
3609,
and 3688 (1968)]
*