  An approach that extends equilibrium thermodynamics principles to
out-of-equilibrium systems is based on the local equilibrium hypothesis.
However, the validity of the a priori assumption of local equilibrium has been
questioned due to the lack of sufficient experimental evidence. In this paper,
we present experimental results obtained from a pure thermodynamic study of the
non-turbulent Rayleigh-B\'enard convection at steady-state to verify the
validity of the local equilibrium hypothesis. A non-turbulent Rayleigh-B\'enard
convection at steady-state is an excellent `model thermodynamic system' in
which local measurements do not convey the complete picture about the spatial
heterogeneity present in the macroscopic thermodynamic landscape. Indeed, the
onset of convection leads to the emergence of spatially stable hot and cold
domains. Our results indicate that these domains while break spatial symmetry
macroscopically, preserves it locally that exhibit room temperature
equilibrium-like statistics. Furthermore, the role of the emergent heat flux is
investigated and a linear relationship is observed between the heat flux and
the external driving force following the onset of thermal convection. Finally,
theoretical and conceptual implications of these results are discussed which
opens up new avenues in the study non-equilibrium steady-states, especially in
complex, soft, and active-matter systems.
