An Overview of Emergent Order in Far-from-equilibrium Driven Systems: From Kuramoto Oscillators to Rayleigh-B\'enard Convection

TL;DR

This paper reviews how different driven non-equilibrium systems like Ising models, Kuramoto oscillators, and Rayleigh-Bénard convection exhibit emergent spatio-temporal order through self-organization, highlighting common fluctuation patterns and underlying mechanisms.

Contribution

It provides a comparative overview of three distinct non-equilibrium systems, identifying shared features and connections in their emergence of order.

Findings

Emergent order arises through self-organization in all three systems.

Non-equilibrium fluctuations follow similar trends across systems.

Connections between different driven systems are identified.

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-B\'enard 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.