Oppenheim Jonathan
Racah Institute of Theoretical Physics, Hebrew University of Jerusalem, Givat Ram, Jerusalem 91904, Israel.
Phys Rev E Stat Nonlin Soft Matter Phys. 2003 Jul;68(1 Pt 2):016108. doi: 10.1103/PhysRevE.68.016108. Epub 2003 Jul 11.
Methods are presented which enables one to analyze the thermodynamics of systems with long-range interactions. Generically, such systems have entropies which are nonextensive (do not scale with the size of the system). We show how to calculate the degree of nonextensivity for such a system. We find that a system interacting with a heat reservoir is in a probability distribution of canonical ensembles. The system still possesses a parameter akin to a global temperature, which is constant throughout the substance. There is also a useful quantity which acts like a local temperatures and it varies throughout the substance. These quantities are closely related to counterparts found in general relativity. A lattice model with long-range spin-spin coupling is studied. This is compared with systems such as those encountered in general relativity and gravitating systems with Newtonian-type interactions. A long-range lattice model is presented which can be seen as a black hole analog. One finds that the analog's temperature and entropy have many properties which are found in black holes. Finally, the entropy scaling behavior of a gravitating perfect fluid of constant density is calculated. For weak interactions, the entropy scales like the volume of the system. As the interactions become stronger, the entropy becomes higher near the surface of the system, and becomes more area scaling.
本文介绍了一种能够分析具有长程相互作用系统热力学的方法。一般来说，这类系统的熵是非广延的（不随系统大小成比例变化）。我们展示了如何计算这类系统的非广延程度。我们发现，与热库相互作用的系统处于正则系综的概率分布中。该系统仍然拥有一个类似于全局温度的参数，它在整个物质中是恒定的。还有一个有用的量，其作用类似于局部温度，并且在整个物质中是变化的。这些量与广义相对论中发现的对应量密切相关。研究了具有长程自旋 - 自旋耦合的晶格模型。将其与广义相对论中遇到的系统以及具有牛顿型相互作用的引力系统进行了比较。提出了一种长程晶格模型，它可以被视为黑洞的类比。人们发现，该类比的温度和熵具有许多在黑洞中发现的性质。最后，计算了恒定密度引力理想流体的熵标度行为。对于弱相互作用，熵的标度类似于系统的体积。随着相互作用变强，系统表面附近的熵变得更高，并且变得更具面积标度性。
