The Many Faces of Far-from-equilibrium Thermodynamics: Deterministic Chaos, Randomness or Emergent Order?

Far-from-equilibrium systems are ubiquitous in nature. They are also rich in terms of diversity and complexity. Therefore, it is an intellectual challenge to be able to understand the physics of far-from-equilibrium phenomena. In this paper we revisit a standard tabletop experiment, the Rayleigh-B{\'e}nard convection, to explore some fundamental questions and present a new perspective from a first-principles point of view. How non-equilibrium fluctuations differ from equilibrium fluctuations, how emergence of order out-of-equilibrium breaks symmetries in the system, or how free-energy of a system gets locally bifurcated to operate a Carnot-like engine to maintain order? The exploration and investigation of these non-trivial questions are the focus of this paper.