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An Overview of Emergent Order in Far-from-Equilibrium Driven Systems: From Kuramoto Oscillators to Rayleigh–Bénard Convection
Entropy ( IF 2.7 ) Pub Date : 2020-05-17 , DOI: 10.3390/e22050561
Atanu Chatterjee , Nicholas Mears , Yash Yadati , Germano S. Iannacchione

Soft-matter systems when driven out of equilibrium often give rise to structures that usually lie in between the macroscopic scale of the material and microscopic scale of its constituents. In this paper we review three such systems, the two-dimensional square-lattice Ising model, the Kuramoto model and the Rayleigh–Bénard convection system which when driven out of equilibrium give rise to emergent spatio-temporal order through self-organization. A common feature of these systems is that the entities that self-organize are coupled to one another in some way, either through local interactions or through a continuous media. Therefore, the general nature of non-equilibrium fluctuations of the intrinsic variables in these systems are found to follow similar trends as order emerges. Through this paper, we attempt to find connections between these systems, and systems in general which give rise to emergent order when driven out of equilibrium. This study, thus acts as a foundation for modeling a complex system as a two-state system, where the states: order and disorder can coexist as the system is driven away from equilibrium.

中文翻译:

远非平衡驱动系统中的紧急顺序概述:从仓本振荡器到瑞利-贝纳德对流

软物质系统在失去平衡时通常会产生结构,这些结构通常介于材料的宏观尺度和其成分的微观尺度之间。在本文中,我们回顾了三个这样的系统,二维方格 Ising 模型、Kuramoto 模型和 Rayleigh-Bénard 对流系统,当它们脱离平衡时,会通过自组织产生涌现的时空秩序。这些系统的一个共同特征是,自组织的实体以某种方式相互耦合,要么通过本地交互,要么通过连续媒体。因此,随着秩序的出现,这些系统中内在变量的非均衡波动的一般性质被发现遵循类似的趋势。通过这篇论文,我们试图找到这些系统之间的联系,以及在被驱赶出平衡时产生紧急秩序的一般系统之间的联系。因此,这项研究是将复杂系统建模为二态系统的基础,其中状态:有序和无序可以在系统远离平衡时共存。
更新日期:2020-05-17
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