Raz T, Levine R D
Azrieli College of Engineering, Jerusalem 91035, Israel.
The Fritz Haber Research Centre for Molecular Dynamics, Institute of Chemistry, The Hebrew University, Jerusalem 91904, Israel.
Proc Natl Acad Sci U S A. 2023 Aug 29;120(35):e2310281120. doi: 10.1073/pnas.2310281120. Epub 2023 Aug 21.
Our information theoretic considerations suggest that the essence of phase transitions in condensed matter is the change in entropy as reflected in the change in the number of isomers between two phases. The explicit number of isomers as a function of size is computed using a graph theoretic approach that is compared to a direct count for smaller systems. This allows us to apply a common approach to both nanosystems and their macroscopic limit. The entropy increases very rapidly with size with the results that replacing the actual distribution over size by an average is not an accurate approximation. That the phase transition is a sharp function of the temperature is due to the high heat capacity of both the solid and liquid phases. The difference in entropy at the transition is related to the Trouton-Richards considerations. The finite width of the boundary between two phases of a finite system is related to the inherent uncertainty product that is derived from the maximum entropy formalism and that is a result of the fluctuations about equilibrium. As the system size increases, the boundary becomes sharper and one recovers the usual thermodynamic description.
我们基于信息论的思考表明，凝聚态物质中相变的本质是熵的变化，这反映在两个相之间异构体数量的变化上。作为尺寸函数的异构体的具体数量是使用图论方法计算的，并与较小系统的直接计数进行比较。这使我们能够将一种通用方法应用于纳米系统及其宏观极限。熵随尺寸迅速增加，结果是用平均值代替实际的尺寸分布并非精确近似。相变是温度的尖锐函数，这是由于固相和液相的高比热容所致。转变时熵的差异与特鲁顿 - 理查兹的考量有关。有限系统的两个相之间边界的有限宽度与从最大熵形式主义导出的固有不确定性乘积有关，这是平衡附近涨落的结果。随着系统尺寸增加，边界变得更清晰，人们恢复到通常的热力学描述。
