An Overview of Emergent Order in Far-from-Equilibrium Driven Systems: From Kuramoto Oscillators to Rayleigh–Bénard Convection

Chatterjee, Atanu; Mears, Nicholas; Yadati, Yash; Iannacchione, Germano S.

doi:10.3390/e22050561

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An Overview of Emergent Order in Far-from-Equilibrium Driven Systems: From Kuramoto Oscillators to Rayleigh–Bénard Convection

Atanu Chatterjee

^*,

Nicholas Mears

Yash Yadati

and

Germano S. Iannacchione

Department of Physics, Worcester Polytechnic Institute, 100 Institute Road, Worcester, MA 01605, USA

Authors to whom correspondence should be addressed.

Entropy 2020, 22(5), 561; https://doi.org/10.3390/e22050561

Received: 16 April 2020 / Revised: 14 May 2020 / Accepted: 15 May 2020 / Published: 17 May 2020

(This article belongs to the Special Issue Thermodynamics of Nonequilibrium Processes)

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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 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. View Full-Text

Keywords: non-equilibrium thermodynamics; Ising model; Kuramoto model; Rayleigh–Bénard convection; pattern formation

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Chatterjee, A.; Mears, N.; Yadati, Y.; Iannacchione, G.S. An Overview of Emergent Order in Far-from-Equilibrium Driven Systems: From Kuramoto Oscillators to Rayleigh–Bénard Convection. Entropy 2020, 22, 561. https://doi.org/10.3390/e22050561

AMA Style

Chatterjee A, Mears N, Yadati Y, Iannacchione GS. An Overview of Emergent Order in Far-from-Equilibrium Driven Systems: From Kuramoto Oscillators to Rayleigh–Bénard Convection. Entropy. 2020; 22(5):561. https://doi.org/10.3390/e22050561

Chicago/Turabian Style

Chatterjee, Atanu, Nicholas Mears, Yash Yadati, and Germano S. Iannacchione. 2020. "An Overview of Emergent Order in Far-from-Equilibrium Driven Systems: From Kuramoto Oscillators to Rayleigh–Bénard Convection" Entropy 22, no. 5: 561. https://doi.org/10.3390/e22050561

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An Overview of Emergent Order in Far-from-Equilibrium Driven Systems: From Kuramoto Oscillators to Rayleigh–Bénard Convection

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