Di Cairano Loris, Gori Matteo, Pettini Marco
Institute of Neuroscience and Medicine INM-9, and Institute for Advanced Simulation IAS-5, Forschungszentrum Jülich, 52428 Jülich, Germany.
Department of Physics, Faculty of Mathematics, Computer Science and Natural Sciences, Aachen University, 52062 Aachen, Germany.
Entropy (Basel). 2021 Oct 27;23(11):1414. doi: 10.3390/e23111414.
Different arguments led to supposing that the deep origin of phase transitions has to be identified with suitable topological changes of potential related submanifolds of configuration space of a physical system. An important step forward for this approach was achieved with two theorems stating that, for a wide class of physical systems, phase transitions should necessarily stem from topological changes of energy level submanifolds of the phase space. However, the sufficiency conditions are still a wide open question. In this study, a first important step forward was performed in this direction; in fact, a differential equation was worked out which describes how entropy varies as a function of total energy, and this variation is driven by the total energy dependence of a topology-related quantity of the relevant submanifolds of the phase space. Hence, general conditions can be in principle defined for topology-driven loss of differentiability of the entropy.
不同的论据导致人们认为，相变的深层起源必须与物理系统构型空间中与势相关的子流形的适当拓扑变化联系起来。对于这种方法而言，向前迈出的重要一步是通过两个定理实现的，这两个定理表明，对于一大类物理系统，相变必然源于相空间能级子流形的拓扑变化。然而，充分条件仍然是一个悬而未决的大问题。在本研究中，朝着这个方向迈出了重要的第一步；事实上，我们推导出了一个微分方程，它描述了熵如何作为总能量的函数而变化，并且这种变化是由相空间相关子流形的一个与拓扑相关的量对总能量的依赖所驱动的。因此，原则上可以为熵的拓扑驱动的可微性丧失定义一般条件。
