Gradient, entropy and entropy fluctation on high DOF systems

(Roberto) #1

I have an idea clear in my mind, but don’t know if I am able to express properly and if it is useful to anyone:
– It is clear that a PREDICTION represents the maximum probability to confirm a configuration from a criterion generating it.
– This otherwise means that the prediction in the domain of configurations represents the lowest possible increase of entropy, matching the instance of the criterion with the observation.
– BUT THIS ALSO MEANS THAT IT REPRESENTS THE MINIMUM FLUCTUATION (I.E. GRADIENT) OF THE ENTROPY IN THE DOMAIN OF PREDICTIONS, REPRESENTING THE CRITERION WHICH ORIGINATED THE PREDICTION ITSELF.
Equivalent to say that the prediction is the derivative domain of the observation domain.

NOTE: In this sense when I talk about orthogonality of DOF by definition I mean that the hosting model has to be big enough to contain all possible independent observable configurations, with the impossibility to project each on each other.

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