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A challenge in fundamental physics and especially in thermodynamics is tounderstand emergent order in far-from-equilibrium systems. While atequilibrium, temperature plays the role of a key thermodynamic variable whoseuniformity 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 flowsthrough a finite system at steady-state, temperature takes on atime-independent but spatially varying character. In this study, the convectionpatterns of a Rayleigh-B{\'e}nard fluid cell at steady-state is used as aprototype system where the temperature profile and fluctuations are measuredspatio-temporally. The thermal data is obtained by performing high-resolutionreal-time infrared calorimetry on the convection system as it is first drivenout-of-equilibrium when the power is applied, achieves steady-state, and thenas it gradually relaxes back to room temperature equilibrium when the power isremoved. Our study provides new experimental data on the non-trivial nature ofthermal fluctuations when stable complex convective structures emerge. Thethermal analysis of these convective cells at steady-state further yield localequilibrium-like statistics. In conclusion, these results correlate the spatialordering of the convective cells with the evolution of the system's temperaturemanifold.

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