Abstract
As first shown by H. S. Green in 1952, the entropy of a classical fluid of identical particles can be written as a sum of many-particle contributions, each of them being a distinctive functional of all spatial distribution functions up to a given order. By revisiting the combinatorial derivation of the entropy formula, we argue that a similar correlation expansion holds for the entropy of a crystalline system. We discuss how one- and two-body entropies scale with the size of the crystal, and provide fresh numerical data to check the expectation, grounded in theoretical arguments, that both entropies are extensive quantities.
Highlights
IntroductionThe entropy multiparticle correlation expansion (MPCE) is an elegant statistical-mechanical formula that entails the possibility of reconstructing the total entropy of a many-particle system term by term, including at each step of summation the integrated contribution from spatial correlations between a specified number of particles
The entropy multiparticle correlation expansion (MPCE) is an elegant statistical-mechanical formula that entails the possibility of reconstructing the total entropy of a many-particle system term by term, including at each step of summation the integrated contribution from spatial correlations between a specified number of particles.The original derivation of the entropy MPCE is found in a book by H
In Appendix A we present another derivation of the entropy formula in the canonical ensemble (CE), which is closer in spirit to the one given by H
Summary
The entropy multiparticle correlation expansion (MPCE) is an elegant statistical-mechanical formula that entails the possibility of reconstructing the total entropy of a many-particle system term by term, including at each step of summation the integrated contribution from spatial correlations between a specified number of particles. Since the original observation in [13], a clear correspondence between the RMPE zero and the ultimate threshold for spatial homogeneity in the system has been found in many simple and complex fluids [14,15,16,17,18,19,20,21,22,23,24], thereby leading to the belief that the vanishing of the RMPE is a signature of an impending structural or thermodynamic transition of the system from a less ordered to a more spatially organized condition (freezing is just an example of many) Albeit empirical, this entropic criterion is a valid alternative to the far more demanding exact free-energy methods when a rough estimate of the transition point is deemed sufficient.
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