What if entropy, rather than a statistical, information theoretic, macroscopic or phenomenological concept, were an intrinsic property of matter in the same sense as energy is universally understood to be an intrinsic property of matter? What if irreversibility were an intrinsic feature of the fundamental dynamical laws obeyed by all physical objects, macroscopic and microscopic, complex and simple, large and small? What if the second law of thermodynamics, in the hierarchy of physical laws, were at the same level as the fundamental laws of mechanics, such as the great conservation principles? Is it inevitable that the gap between mechanics and thermodynamics be bridged by resorting to the usual statistical, phenomenological, or information-theoretic reasoning, and by hinging on the hardly definable distinction between microscopic and macroscopic reality? Is it inevitable that irreversibility be explained by designing ad hoc mechanisms of coupling with some heat bath, reservoir or environment, and ad hoc mechanisms of loss of correlation? What if, instead, mechanics and thermodynamics were both special cases of a more general unified fundamental physical theory valid for all systems, including a single strictly isolated particle, such as a single isolated harmonic oscillator or a single isolated two-level spin system?