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

## TL;DR

This study investigates the complex thermal and structural behaviors of Rayleigh-Bénard convection at steady-state, revealing coexisting ordered states, local equilibrium-like domains, and broken ergodicity through high-resolution infrared calorimetry.

## Contribution

It provides new experimental insights into the non-trivial thermal fluctuations and spatial ordering in non-turbulent convection systems at steady-state, highlighting emergent order far from equilibrium.

## Key findings

- Identification of coexisting ordered states in convection patterns
- Observation of local equilibrium-like thermal statistics
- Correlation between spatial order and temperature evolution

## 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-B{\'e}nard 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.