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"Density fluctuations and entropy"
J.A. Hernando and L. Blum
Phys. Rev. E 62(5) (2000) 6577-6583
A new 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 new term S(c) depends on the p-bodies density fluctuations αp and 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 proven: 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 new numerical expression for the entropy with a new 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.
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