Statistical mechanical models with effective potentials: Definitions, applications, and thermodynamic consequences
Statistical mechanical models with effective potentials: Definitions, applications, and thermodynamic consequences
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具有有效潜力的统计力学模型：定义、应用和热力学后果
DOI：
10.1063/1.1480863
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发表时间：
2002
影响因子：
4.4
通讯作者：
S. Torquato
中科院分区：
文献类型：
--
作者：
F. Stillinger;H. Sakai;S. Torquato
在凝聚态系统中运行的现实相互作用可能会表现出复杂的多粒子特征。然而，为了利用由此产生的理论和计算简化，寻求更经济的描述通常是有用的，即最多使用与密度相关的单态和成对有效相互作用。本文分析了用这种方法描述热平衡所需的统计力学形式。对于密度依赖的作用，有两种不同的解释。其中任何一个都可以用内部一致性来处理，但通常它们会导致不同的热力学预测。人们认为有效相互作用的密度依赖性仅仅是确定这些有效相互作用的最佳选择的状态的被动指数(情况一)。另一种将密度视为与粒子坐标相同的主动变量(第二种情况)。给出了两种情况下的维里压力和等温压缩系数的颗粒分布函数表达式。在特殊情况下，两种解释产生相同的压力等温线是可能的；用密度展开的方法探索了产生这种一致的条件。
Realistic interactions that operate in condensed matter systems can exhibit complicated many-particle characteristics. However, it is often useful to seek a more economical description using at most singlet and pair effective interactions that are density dependent, to take advantage of the theoretical and computational simplifications that result. This paper analyzes the statistical mechanical formalism required to describe thermal equilibrium in that kind of approach. Two distinct interpretations are available for the role of density dependence. Either one can be treated with internal consistency, but generally they lead to differing thermodynamic predictions. One regards the density dependence of effective interactions as merely a passive index for the state at which the optimal choice of those effective interactions was determined (Case I). The other treats the density as an active variable on the same footing as particle coordinates (Case II). Virial pressure and isothermal compressibility expressions in terms of particle distribution functions are displayed for both cases. Under special circumstances it is possible for the two interpretations to yield the same pressure isotherms; the conditions producing this coincidental concordancy have been explored by means of density expansions.