#### apeiron

Gold Member

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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.

/Fredrik

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.