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1. Controlling conservation laws I: Entropy–entropy flux

   https://doi.org/10.1016/j.jcp.2023.112019  

   Li, Wuchen; Liu, Siting; Osher, Stanley (May 2023, Journal of Computational Physics)
2. Disordered enthalpy–entropy descriptor for high-entropy ceramics discovery

   https://doi.org/10.1038/s41586-023-06786-y  

   Divilov, Simon; Eckert, Hagen; Hicks, David; Oses, Corey; Toher, Cormac; Friedrich, Rico; Esters, Marco; Mehl, Michael J; Zettel, Adam C; Lederer, Yoav; et al (January 2024, Nature)

   Abstract The need for improved functionalities in extreme environments is fuelling interest in high-entropy ceramics^1–3. Except for the computational discovery of high-entropy carbides, performed with the entropy-forming-ability descriptor⁴, most innovation has been slowly driven by experimental means^1–3. Hence, advancement in the field needs more theoretical contributions. Here we introduce disordered enthalpy–entropy descriptor (DEED), a descriptor that captures the balance between entropy gains and enthalpy costs, allowing the correct classification of functional synthesizability of multicomponent ceramics, regardless of chemistry and structure. To make our calculations possible, we have developed a convolutional algorithm that drastically reduces computational resources. Moreover, DEED guides the experimental discovery of new single-phase high-entropy carbonitrides and borides. This work, integrated into the AFLOW computational ecosystem, provides an array of potential new candidates, ripe for experimental discoveries. 

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3. On discretely entropy conservative and entropy stable discontinuous Galerkin methods

   https://doi.org/10.1016/j.jcp.2018.02.033  

   Chan, Jesse (June 2018, Journal of Computational Physics)
4. Temperature-Dependent Configurational Entropy Calculations for Refractory High-Entropy Alloys

   https://doi.org/10.1007/s11669-021-00879-9  

   Nataraj, Chiraag M; van de Walle, Axel; Samanta, Amit (April 2021, Journal of Phase Equilibria and Diffusion)

   null (Ed.)

   The cluster expansion formalism for alloys is used to construct surrogate models for three refractory high-entropy alloys (NbTiVZr, HfNbTaTiZr, and AlHfNbTaTiZr). These cluster expansion models are then used along with Monte Carlo methods and thermodynamic integration to calculate the configurational entropy of these refractory high-entropy alloys as a function of temperature. Many solid solution alloy design guidelines are based on the ideal entropy of mixing, which increases monotonically with N, the number of elements in the alloy. However, our results show that at low temperatures, the configurational entropy of these materials is largely independent of N, and the assumption described above only holds in the high-temperature limit. This suggests that alloy design guidelines based on the ideal entropy of mixing require further examination. 

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5. Stabilizer Rényi Entropy

   https://doi.org/10.1103/PhysRevLett.128.050402  

   Leone, Lorenzo; Oliviero, Salvatore F. E.; Hamma, Alioscia (February 2022, Physical Review Letters)