Spatio-temporal characterization of thermal fluctuations in a non-turbulent Rayleigh–Bénard convection at steady state

Abstract

In this paper we present a detailed description of the statistical and computational techniques that were employed to study a driven far-from-equilibrium steady-state Rayleigh-Bénard system in the non-turbulent regime (Ra ≤ 3500). In our previous work on the Rayleigh-Bénard convection system we try to answer two key open problems that are of great interest in contemporary physics: (i) how does an out-of-equilibrium steady-state differ from an equilibrium state and (ii) how do we explain the spontaneous emergence of stable structures and simultaneously interpret the physical notion of temperature when out-of-equilibrium. We believe that this paper will offer a useful repository of the technical details for a first principles study of similar kind. In addition, we are also hopeful that our work will spur considerable interest in the community which will lead to the development of more sophisticated and novel techniques to study far-from-equilibrium behavior. arXiv:1905.08761v1 [cond-mat.soft]

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.…”

“…These stable spatial gradients lead to the emergence of two local equilibrium-like regions, fluctuations within which can be best represented by respective Gaussian distributions [16].…”

Time and thermodynamics extended discussion on “Time & clocks: A thermodynamic approach”

“…The out-of-equilibrium system thus locks itself in these local equilibrium states while dissipating heat into the surrounding and giving rise to emergent structural complexities, for example, the Rayeligh-Bénard convection. Under such circumstances the spatial variation of the entropy and temperature are crucial which we have discussed in our previous works [10,11,15,16]. Finally, the authors discuss the consequence of relativistic effect on temperature.…”