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Abstract Today’s thermodynamics is largely based on the combined law for equilibrium systems and statistical mechanics derived by Gibbs in 1873 and 1901, respectively, while irreversible thermodynamics for nonequilibrium systems resides essentially on the Onsager Theorem as a separate branch of thermodynamics developed in 1930s. Between them, quantum mechanics was invented and quantitatively solved in terms of density functional theory (DFT) in 1960s. These three scientific domains operate based on different principles and are very much separated from each other. In analogy to the parable of the blind men and the elephant articulated by Perdew, they individually represent different portions of a complex system and thus are incomplete by themselves alone, resulting in the lack of quantitative agreement between their predictions and experimental observations. Over the last two decades, the author’s group has developed a multiscale entropy approach (recently termed as zentropy theory) that integrates DFT-based quantum mechanics and Gibbs statistical mechanics and is capable of accurately predicting entropy and free energy of complex systems. Furthermore, in combination with the combined law for nonequilibrium systems presented by Hillert, the author developed the theory of cross phenomena beyond the phenomenological Onsager Theorem. The zentropy theory and theory of cross phenomena jointly provide quantitative predictive theories for systems from electronic to any observable scales as reviewed in the present work. 

Unraveling mechanical properties from fundamentals is far from complete despite their vital role in determining applicability and longevity for a given material. Here, we perform a comprehensive study related to mechanical properties of 60 pure elements in bcc, fcc, hcp, and/or diamond structures by means of pure alias shear and pure tensile deformations via density functional theory (DFT) based calculations alongside a broad review of existing literature. The present data compilation enables a detailed correlation analysis of mechanical properties, focusing on DFT-based ideal shear and tensile strengths (τis and σit), stable and unstable stacking fault energies (γsf and γus), surface energy (γs), and vacancy activation energy (QV); and experimental hardness (HB), ultimate tensile strength (σUT), fracture toughness (KIc), and elongation (εEL). The present work examines models, identifies outliers, and provides insights into mechanical properties, for example, (i) HB is correlated by QV, σUT by γs or γus, and KIc by γs; (ii) data outliers are identified for Cr (related to τis, γs, QV, and σUT), Be (τis, γsf, γus, and QV), Hf (HB and KIc), Yb (all properties), and Pt (γsf vs. γus); and (iii) τis σit, γsf, γus, γs, QV, and HB are highly correlated to elemental attributes, while σUT, KIc, and especially εEL are less correlated due mainly to experimental uncertainty. In particular, the present data compilation provides a solid foundation to model properties such as γs and τis of multicomponent alloys and τis of unstable structures like bcc Ti, Zr, and Hf.