Phase transitions in complex systems : An information geometric approach
Phase transitions in complex systems : An information geometric approach
复制标题
复杂系统中的相变：信息几何方法
DOI：
--
复制
发表时间：
2017
期刊：
影响因子：
--
通讯作者：
Har Shemesh
中科院分区：
文献类型：
--
作者：
Har Shemesh
我们生活在一个复杂的世界。无论我们观察反应堆中的化学反应，大脑中的神经元网络，还是人类社会，都会看到一个迷人的多层次非线性系统。复杂性领域将研究这些系统的共同点作为一个目标，这些系统通常在不同的学科中单独研究。由于复杂性研究的前提是存在一个共同点，因此出现了一个问题，即可以将这些现象统一起来的概念和数学框架是什么。在我的论文中，我探索的可能性，在复杂系统中的关键现象可以使用一个框架，称为信息几何研究。这个想法是从几何统计力学借来的，在几何统计力学中，许多模型的信息几何表现出相变已经被研究，一些研究人员甚至提出了几何性质作为临界转变的定义。直觉很简单-当一个系统用统计术语描述时，它的不同阶段总是具有不同的统计特性。这些性质的突变可以用来定义相变线。反过来说，我们可以把这个问题称为一个推理问题--给定系统的统计特性，我们能在多大程度上测量控制过渡的基本控制参数。在统计性质变化较大的相变点，参数的值很容易推断。因此，可以使用Fisher信息来检测相变。
We live in a complex world. Whether we look at chemical reactions in a reactor, networks of neurons in the brain, or human societies, a fascinating multi-level, non-linear system appears. The field of complexity has set it as a goal to study the common denominator of these systems, which are usually studied separately in disparate academic disciplines. Since the premise of complexity research is that there exists a common denominator, a question arises about what will be the conceptual and mathematical framework that can unite these phenomena. In my thesis I explore the possibility that critical phenomena in complex systems can be studied using a framework called Information Geometry. The idea is borrowed from geometrical statistical mechanics where the information geometry of many models exhibiting phase transitions have been studied and some researchers have even gone so far as to suggest the geometrical properties as a definition for critical transitions. The intuition is simple – when a system is described in statistical terms, its different phases will invariably have different statistical properties. The sudden change in these properties can be used to define the phase transition line. Inverting the question one can term this as an inference problem – given the statistical properties of the system, how well can we measure the underlying control parameters that govern the transition. At the phase transition point, where the change in statistical properties is large, the value of the parameter is easy to infer. Therefore one can use the Fisher information to detect the phase transition.
影响因子：
8.6
作者：
Schwab DJ;Nemenman I;Mehta P
通讯作者：
Mehta P