Glad it is soft bits after all! And soft contexts too! Actually, I should call the difference vague-crisp rather than soft-hard as this would be the more appropriate jargon.Yes, except of course that there are only equilibriums at each level, here is no fixed microstructure to which equilibrium refers.
And while I agree we would be talking about equilibriums at every level, I think the next crucial point is that there is then only one value for the resulting overall systems equilibrium - its Lyapunov exponent so to speak.
So across all scales, the universe's information/observerhood must be thermalised. A single temperature rules.
But where this gets tricky is that the universe is of course an expanding space. It is not a static system, closed in scale, but a dynamic system, open in scale.
So the right statistics is not the usual gaussian model of a closed system but the powerlaw or fractal statistics of a scale free system. The "temperature" is not damped around a single mean value but is expressed flatly - log/log fashion - over all scales. Hence the Lyapunov exponent analogy.
Basically, this all needs a modern open systems model of entropy, perhaps like Renyi or Tsallis non-extensive models. A fractal equilibrium model with an emergent axis of scale rather than a damped gaussian equilibrium such as is only possible inside a closed box.