Topological extension of the isomorph theory based on the Shannon entropy

Tae Jun Yoon, Min Young Ha, Emanuel A. Lazar, Won Bo Lee, Youn Woo Lee

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12 Scopus citations


Isomorph theory is one of the promising theories for understanding the quasiuniversal relationship between thermodynamic, dynamic, and structural characteristics. Based on the hidden scale invariance of the inverse power law potentials, it rationalizes the excess entropy scaling law of dynamic properties. This work aims to show that this basic idea of isomorph theory can be extended by examining the microstructural features of the system. Using the topological framework in conjunction with the entropy calculation algorithm, we demonstrate that Voronoi entropy, a measure of the topological diversity of single atoms, provides a scaling law for the transport properties of soft-sphere fluids, which is comparable to the frequently used excess entropy scaling. By examining the relationship between the Voronoi entropy and the solidlike fraction of simple fluids, we suggest that the Frenkel line, a rigid-nonrigid crossover line, be a topological isomorphic line at which the scaling relation qualitatively changes.

Original languageEnglish
Article number012118
JournalPhysical Review E
Issue number1
StatePublished - 15 Jul 2019

Bibliographical note

Funding Information:
M.Y.H. and W.B.L. acknowledge support by the Creative Materials Discovery Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science and ICT (2018M3D1A1058624). E.A.L. gratefully acknowledges the generous support of the US National Science Foundation through Award No. DMR-1507013.

Publisher Copyright:
© 2019 American Physical Society.


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