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In this paper we present a detailed description of the statistical andcomputational techniques that were employed to study a drivenfar-from-equilibrium steady-state Rayleigh-B{\'e}nard system in thenon-turbulent regime ($Ra\leq 3500$). In our previous work on theRayleigh-B{\'e}nard convection system we try to answer two key open problemsthat are of great interest in contemporary physics: (i) how does anout-of-equilibrium steady-state differ from an equilibrium state and (ii) howdo we explain the spontaneous emergence of stable structures and simultaneouslyinterpret the physical notion of temperature when out-of-equilibrium. Webelieve that this paper will offer a useful repository of the technical detailsfor a first principles study of similar kind. In addition, we are also hopefulthat our work will spur considerable interest in the community which will leadto the development of more sophisticated and novel techniques to studyfar-from-equilibrium behavior.

Spatio-temporal Characterization of Thermal Fluctuations in a Non-turbulent Rayleigh-B\'enard Convection at Steady State