The statistical thermodynamics of a classical system composed of rigid molecules is considered in the molecular dynamics ensemble. Accepting Boltzmann’s S=kB ln W as the basic assumption of statistical mechanics, exact formalisms for two classical choices of W are derived. Since there are no restrictions on the order of thermodynamic derivatives, any measurable quantity is directly accessible in this ensemble. Explicit statistical analogs are given for the derivatives of the Helmholtz energy including an approximation for the chemical potential. Basic phase space functions are identified and their properties are explored. It is shown that the complete thermodynamics is governed by small perturbations of these functions from universal behavior.  

1.
M. P. Allen and D. J. Tildesley, Computer Simulation of Liquids (Clarendon, Oxford, 1987).
2.
W. G. Hoover, Computational Statistical Mechanics, Studies in Modern Thermodynamics 11 (Elsevier, Amsterdam, 1991).
3.
T. L. Hill, Statistical Mechanics (McGraw-Hill, New York, 1956), p. 71.
4.
K. Huang, Statistical Mechanics, 2nd ed. (Wiley, New York, 1987), p. 140.
5.
Reference 1, p. 47.
6.
Reference 2, Chap. 3.4.
7.
J. L.
Lebowitz
,
J. K.
Percus
, and
L.
Verlet
,
Phys. Rev.
153
,
250
(
1967
).
8.
E. M.
Pearson
,
T.
Halicioglu
, and
W. A.
Tiller
,
Phys. Rev. A
32
,
3030
(
1985
).
9.
A. Münster, Statistische Thermodynamik (Springer, Berlin, 1956), Chaps. 5.11 and 5.12.
10.
T.
Çaǧin
and
J. R.
Ray
,
Phys. Rev. A
37
,
247
(
1988
).
11.
J. M. Haile, Molecular Dynamics Simulation. Elementary Methods (Wiley, New York, 1992).
12.
M.
Litniewski
,
J. Phys. Chem.
94
,
6472
(
1990
).
13.
Reference 4, Chap. 6.
14.
C. G. Gray and K. E. Gubbins, Theory of Molecular Fluids Vol. 1, Fundamentals (Clarendon, Oxford, 1984), Appendix 3A.
15.
I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products (Academic, Orlando, 1980), Chap. 3.3–3.4.
16.
J. E. Mayer and M. Goeppert Mayer, Statistical Mechanics, 2nd ed. (Wiley, New York, 1977), p. 200.
17.
R. Becker, Theorie der Wärme, 3rd ed. (Springer, Berlin, 1985), Chap. 36.
18.
More precisely, since, even though periodic boundary conditions are usually employed, the total number of degrees of freedom is small.
19.
The choice of these state functions as basic quantities is also of importance for devising proper cutoff corrections (cf. part II of this series).
20.
Reference 14, Appendix 3C.
21.
J. S. Rowlinson and F. L. Swinton, Liquids and Liquid Mixtures, 3rd ed. (Butterworths, London, 1982), Chap. 2.
22.
R.
Schmidt
and
W.
Wagner
,
Fluid Phase Equilibria
19
,
175
(
1985
).
23.
D. Frenkel, in Proceedings of the 97th International “Enrico Fermi” School of Physics, Varenna, 1985, edited by G. Ciccotti and W. G. Hoover (North-Holland, Amsterdam, 1985).
24.
(a)
B.
Widom
,
J. Chem. Phys.
39
,
2808
(
1963
);
lpar;b)
B.
Widom
,
J. Phys. Chem.
86
,
869
(
1982
).
25.
Since the formulas become increasingly lengthy, the development given here is restricted to order four. An extended list of results can be found in R. Lustig, Habilitation-thesis, RWTH, 1993.
26.
A. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1970), Chap. 24.
This content is only available via PDF.
You do not currently have access to this content.