TY - JOUR

T1 - Structural degeneracy in pair distance distributions

AU - Stillinger, Frank H.

AU - Torquato, Salvatore

N1 - Funding Information:
The authors are grateful to Timothy Middlemas for figure preparation assistance. This work was supported partially by the National Science Foundation under Grant No. CBET-1701843.
Publisher Copyright:
© 2019 Author(s).

PY - 2019/5/28

Y1 - 2019/5/28

N2 - A traditional basic descriptor of many-particle systems has been the distribution of interparticle pair distances. In the case of structureless particles at thermal equilibrium, with just additive pair interactions, this suffices to determine pressure and mean energy. However, it is usually the case that a given set of pair distances can emerge from a multiplicity of distinguishable many-particle configurations. This paper focuses on the ways in which such a configuration detail can be overlooked. After providing some elementary small-system examples in which full pair distance specification still permits distinct configurational pattern ambiguity, subsequent analysis concentrates on large-system classical canonical ensembles. In that context, configurational degeneracy is analyzed in two-dimensional systems for the shape distribution of triangles, whose chirality occurrence can be controlled by suitable three-particle interactions. For many-particle systems in three dimensions, the possibility is explored that a set of three-particle "pair-invisible" interactions can exist which modify the three-particle distribution function, but which have no effect on the pair distribution function, and thus remain undetected by conventional diffraction experiments. For illustration, a specific mathematical example is presented, applicable to the case where two-particle interactions vanish.

AB - A traditional basic descriptor of many-particle systems has been the distribution of interparticle pair distances. In the case of structureless particles at thermal equilibrium, with just additive pair interactions, this suffices to determine pressure and mean energy. However, it is usually the case that a given set of pair distances can emerge from a multiplicity of distinguishable many-particle configurations. This paper focuses on the ways in which such a configuration detail can be overlooked. After providing some elementary small-system examples in which full pair distance specification still permits distinct configurational pattern ambiguity, subsequent analysis concentrates on large-system classical canonical ensembles. In that context, configurational degeneracy is analyzed in two-dimensional systems for the shape distribution of triangles, whose chirality occurrence can be controlled by suitable three-particle interactions. For many-particle systems in three dimensions, the possibility is explored that a set of three-particle "pair-invisible" interactions can exist which modify the three-particle distribution function, but which have no effect on the pair distribution function, and thus remain undetected by conventional diffraction experiments. For illustration, a specific mathematical example is presented, applicable to the case where two-particle interactions vanish.

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U2 - 10.1063/1.5096894

DO - 10.1063/1.5096894

M3 - Article

C2 - 31153177

AN - SCOPUS:85066779866

SN - 0021-9606

VL - 150

JO - Journal of Chemical Physics

JF - Journal of Chemical Physics

IS - 20

M1 - 204125

ER -