Failure of the Volume Function in Granular Statistical Mechanics and an Alternative Formulation.
Failure of the Volume Function in Granular Statistical Mechanics and an Alternative Formulation.
复制标题
粒状统计力学中体积函数的失败和替代公式。
DOI：
10.1103/physrevlett.116.148001
复制
发表时间：
2016
影响因子：
8.6
通讯作者：
Blumenfeld R
中科院分区：
文献类型：
--
作者：
Blumenfeld R
我们首先表明，目前公认的颗粒物质的统计力学是有缺陷的。原因是它是基于体积函数，它只依赖于所有结构自由度的一小部分，并且不受大多数构型微观状态的影响。因此，常用的配分函数严重低估了熵。然后，我们提出了一个新的配方，取代aconnectivityfunction依赖于所有的结构自由度和帐户正确的整个熵的体积函数。我们讨论了新的形式主义的优点，并得出明确的结果，二维和三维系统。我们通过计算实验二维系统的熵来测试形式主义，作为系统大小的函数，并表明它是一个广泛的变量。
We first show that the currently accepted statistical mechanics for granular matter is flawed. The reason is that it is based on the volume function, which depends only on a minute fraction of all the structural degrees of freedom and is unaffected by most of the configurational microstates. Consequently, the commonly used partition function underestimates the entropy severely. We then propose a new formulation, replacing the volume function with aconnectivityfunction that depends on all the structural degrees of freedom and accounts correctly for the entire entropy. We discuss the advantages of the new formalism and derive explicit results for two- and three-dimensional systems. We test the formalism by calculating the entropy of an experimental two-dimensional system, as a function of system size, and showing that it is an extensive variable.