叠熵理论：从材料基因到材料性能

廖名情, 王毅, 王义, 商顺利, 刘梓葵

Zentropy Theory: Bridging Materials Gene to Materials Properties

LIAO Mingqing, WANG William Yi, WANG Yi, SHANG Shun-Li, LIU Zi-Kui

表1 叠熵理论框架与经典统计力学下热力学物理量的比较^[41]

Table 1 Comparison of thermodynamic terminology between zentropy theory and classic statistical mechanics^[41]

Property	Statistical mechanics	Zentropy framework
Entropy	$S = - k_{B} \sum_{k} p^{k} l n p^{k}$	$S = \sum_{k} p^{k} S^{k} - k_{B} \sum_{k} p^{k} l n p^{k}$
Free energy	$F = \sum_{k} p^{k} E^{k} + k_{B} T \sum_{k} p^{k} l n p^{k}$	$F = \sum_{k} p^{k} F^{k} + k_{B} T \sum_{k} p^{k} l n p^{k}$
Partition function	$Z = e x p (- \frac{F}{k_{B} T}) = \sum_{k} e x p (- \frac{E^{k}}{k_{B} T})$	$Z = e x p (- \frac{F}{k_{B} T}) = \sum_{k} e x p (- \frac{F^{k}}{k_{B} T})$
Probability	$p^{k} = \frac{Z^{k}}{Z} = e x p {(- \frac{E^{k} - F}{k_{B} T})}^{}$	$p^{k} = \frac{Z^{k}}{Z} = e x p (- \frac{F^{k} - F}{k_{B} T})$