Cavity Volume and Free Energy in Many-Body Systems
Cavity Volume and Free Energy in Many-Body Systems
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DOI：
10.1007/s00332-021-09744-y
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发表时间：
2021-04
影响因子：
3
通讯作者：
Jamie M. Taylor;Thomas G. Fai;E. Virga;Xiaoyu Zheng;P. Palffy-Muhoray
中科院分区：
文献类型：
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作者：
Jamie M. Taylor;Thomas G. Fai;E. Virga;Xiaoyu Zheng;P. Palffy-Muhoray
在这项工作中，我们推导并分析了热力学极限下单物质系统的自由能表达式，以广义空腔体积表示，该表达式通常是精确的，原则上适用于整个密度范围内的系统，以及通用坐标空间内的粒子。这提供了一个通用的状态方程，因此可以将腔体积与经典结果（例如迈耶的簇展开）联系起来。通过这一点，我们能够深入了解空腔体积和自由能密度之间的联系及其后果。 我们使用允许显式计算的示例来进一步探讨这些结果，恢复经典唐克斯气体的精确结果，并为单一物种、各向同性系统提供 Onsager 自由能的新颖推导。考虑到问题的复杂性，我们还提供了一个在一维上精确的局部晶格模拟，用它我们可以近似硬球系统的空腔体积，以在硬盘和球体处于稀释状态以及超出冻结转变的情况下提供精确的状态方程。
Within this work, we derive and analyse an expression for the free energy of a single-species system in the thermodynamic limit in terms of a generalised cavity volume, that is exact in general, and in principle applicable to systems across their entire range of density, as well as to particles within a general coordinate space. This provides a universal equation of state, and can thus relate the cavity volume to classical results, such as Mayer’s cluster expansions. Through this, we are able to provide some insight into the connections between cavity volume and free energy density, as well as their consequences. We use examples which permit explicit computations to further probe these results, reclaiming the exact results for a classical Tonks gas and providing a novel derivation of Onsager’s free energy for a single species, isotropic system. Given the complexity of the problem, we also provide a local lattice ansatz, exact in one dimension, with which we may approximate the cavity volume for hard sphere systems to provide an accurate equation of state in the cases of hard disks and spheres in both dilute regimes as well as beyond the freezing transition.