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An Overview of Emergent Order in Far-from-Equilibrium Driven Systems: From Kuramoto Oscillators to Rayleigh-Bénard Convection
Version 1
: Received: 25 December 2019 / Approved: 25 December 2019 / Online: 25 December 2019 (06:56:02 CET)
A peer-reviewed article of this Preprint also exists.
Abstract
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 Rayeligh-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-assemble 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 look for connections between among these systems and systems in general which give rise to emergent order when driven out-of-equilibrium.
Keywords
non-equilibrium thermodynamics; Ising model; Kuramoto model; Rayleigh-Bénard convection; pattern formation
Subject
Physical Sciences, Condensed Matter Physics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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