Coexisting Ordered States, Local Equilibrium-like Domains, and Broken Ergodicity in a Non-turbulent Rayleigh-Bénard Convection at Steady-state

Abstract

A challenge in fundamental physics and especially in thermodynamics is to understand emergent order in far-from-equilibrium systems. While at equilibrium, temperature plays the role of a key thermodynamic variable whose uniformity in space and time defines the equilibrium state the system is in, this is not the case in a far-from-equilibrium driven system. When energy flows through a finite system at steady-state, temperature takes on a time-independent but spatially varying character. In this study, the convection patterns of a Rayleigh-Bénard fluid cell at steady-state is used as a prototype system where the temperature profile and fluctuations are measured spatio-temporally. The thermal data is obtained by performing high-resolution real-time infrared calorimetry on the convection system as it is first driven out-of-equilibrium when the power is applied, achieves steady-state, and then as it gradually relaxes back to room temperature equilibrium when the power is removed. Our study provides new experimental data on the non-trivial nature of thermal fluctuations when stable complex convective structures emerge. The thermal analysis of these convective cells at steady-state further yield local equilibrium-like statistics. In conclusion, these results correlate the spatial ordering of the convective cells with the evolution of the system’s temperature manifold.

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

“…The results are then compared with an experimental system, the Rayleigh-Bénard convection for different fluid mixtures at varying Rayleigh numbers (10 3 − 10 6 ). Our study indicates that the nature of emergent order, and the second statistical moment of the respective intrinsic variables follow similar trends across the three systems [14][15][16].…”

“…We are still unsure of the fact that how the fit functions from the two tails merge into one another. In some of our recent works we discuss the presence of a mixture of local equilibrium regions in the Rayleigh-Bénard convection which describes the bimodal nature of the thermal fluctuations [14][15][16]. To conclude, in the mean-field Kuramoto model the final synchronous state being unique allows for the existence of a sharply peaked delta-type distribution, which in reality is best illustrated by a Lorentizian fit.…”

“…While the temporal study allows us to envision the evolution of order in the system, the spatial study lets us visualize how order is spatially distributed through emergent length-scales. One can find more details on the study: the experiments and the analyses here [15,16]. In this section we discuss the results from our numerical simulations and the experimental study.…”

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

“…Since the focus of this study lies in the search for simple modeling tools to understand pattern formation in a complex system, the choice of our model systems is not random. In our previous studies, we had shown how the mean temperature of the top layer of the fluid film bifurcates into ‘hot’ and ‘cold’ domains as a steady-steady is achieved in a non-turbulent Rayleigh–Bénard system [ 19 , 20 , 21 ]. The coexistence of two states, hot and cold, draws similarities to the Ising model which has been successfully used to understand many two-state systems/processes.…”

“…While the temporal study allows us to envision the evolution of order in the system, the spatial study lets us visualize how order is spatially distributed through emergent length-scales. One can find more details on the study: the experiments and the analyses here [ 20 , 21 ].…”