Density fluctuations and entropy
A functional for the entropy that is asymptotically correct both in the high- and low-density limits is proposed. The new form is S=S((id))+S((ln))+S((r))+S((c)), where the term S((c)) depends on the p-body density fluctuations alpha(p) and has the form S((c))/k=<N>ln 2-1+ summation operator(infinity)(p=2) (ln 2)(p)/p! alpha(p)-[exp(alpha(2)-1)-alpha(2)]+Sinsertion mark. Sinsertion mark renormalizes the ring approximation S((r)). This result is obtained by analyzing the functional dependence of the most general expression of the entropy. Two main results for S((c)) are proved: (i) In the thermodynamic limit it is only a functional of the one-body distribution function and (ii) by summing to infinite order the leading contributions in the density a numerical expression for the entropy [Eq. (33)] with a renormalized ring approximation is obtained. The relation of these results to the incompressible approximation for the entropy is discussed and preliminary numerical results on hard spheres are presented.
Hernando
JA
Department of Physics, Comision Nacional de Energia Atomica, Avenida del Libertador 8250, 1429 Buenos Aires, Argentina.
Blum
L