Eriçok O B, Mason J K
Materials Science and Engineering, University of California, Davis, California 95616, USA.
Phys Rev E. 2023 Jun;107(6-1):064107. doi: 10.1103/PhysRevE.107.064107.
As phenomena that necessarily emerge from the collective behavior of interacting particles, phase transitions continue to be difficult to predict using statistical thermodynamics. A recent proposal called the topological hypothesis suggests that the existence of a phase transition could perhaps be inferred from changes to the topology of the accessible part of the configuration space. This paper instead suggests that such a topological change is often associated with a dramatic change in the configuration space geometry, and that the geometric change is the actual driver of the phase transition. More precisely, a geometric change that brings about a discontinuity in the mixing time required for an initial probability distribution on the configuration space to reach the steady state is conjectured to be related to the onset of a phase transition in the thermodynamic limit. This conjecture is tested by evaluating the diffusion diameter and ε-mixing time of the configuration spaces of hard-disk and hard-sphere systems of increasing size. Explicit geometries are constructed for the configuration spaces of these systems and numerical evidence suggests that a discontinuity in the ε-mixing time coincides with the solid-fluid phase transition in the thermodynamic limit.
作为相互作用粒子集体行为必然产生的现象，相变仍然很难用统计热力学来预测。最近提出的一种称为拓扑假设的观点认为，相变的存在或许可以从构型空间可及部分拓扑结构的变化中推断出来。本文则认为，这种拓扑变化通常与构型空间几何结构的剧烈变化相关联，并且几何结构的变化才是相变的实际驱动因素。更确切地说，构型空间上初始概率分布达到稳态所需的混合时间出现不连续的几何结构变化，被推测与热力学极限下相变的发生有关。通过评估尺寸不断增加的硬磁盘和硬球系统构型空间的扩散直径和ε - 混合时间，对这一推测进行了检验。为这些系统的构型空间构建了明确的几何结构，数值证据表明，ε - 混合时间的不连续与热力学极限下的固 - 液相变相吻合。
