On the origin and the evolution of information in the Universe

In summary: But the particles themselves are gone. How can we measure their information?In summary, this tentative note summarizes the origin and the evolution of information in the universe. The information is conserved according to the unitarity principle and conformal to the Liouville Theorem. However, as soon as an irreversible interaction or transition occurs, ie a measurement or a computation operation is made on the system, or if a decoherence process sets in, the hidden quantum information is extracted and spread out to the outside macroscopic world. In information communication/transmission systems, the information acquired through info processing is evaluated by Shannon's Information Theory, ie by his formula for the Information Entropy H(X) as a sum of probabilities, where
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[Mentor Note -- thread moved from the schoolwork forums to the technical forums]

Homework Statement:: Tentative Note and summary on the origin and the evolution of information in the universe.
Relevant Equations:: none

As a teacher of physics I got many questions asked by my students when aboarding the subject of information in quantum mechanics and the content of information in the universe. Based on my reading of articles and papers and participating in blogs (including the PF-Blog) I wrote down the following tentative summary about this topic. Please can you as a specialist who knows details about this subject check if my statements are correct and/or if you need to improve the text. My aim is to forward this summary to my students.

Tentative Note on the origin and the evolution of information in the universe.

In a closed quantum system the quantum information is conserved (in Hilbert space) according to the unitarity principle and conformal to the Liouville Theorem. As soon as an irreversible interaction or transition occurs, ie a measurement or a computation operation is made on the system, or if a decoherence process sets in, the hidden quantum information is extracted and spread out to the outside macroscopic world.

In information communication/transmission systems, the information acquired through info processing is evaluated by Shannon's Information Theory, ie by his formula for the Information Entropy H(X) as a sum of probabilities, where H(X) is a measure of uncertainty or of "hidden Information" in the system.

The amount of emergent (classical) information increases locally and becomes available as knowledge to an observer according to the probabilistic Born Rule and at the cost of local thermodynamic entropy increase according to the Landauer Principle. As the emergent information gets entangled with the environment the increasing correlations result in a degradation of the information in the universe with time.

Or one could say that the information is still there in a different form, but is no longer accessible to observers. As a result the complexity in the universe first increases, attains a maximum and then decreases with time. Thus quantum information must have already existed at the Big Bang, and could have been generated by the decay of the inflaton at the end of the inflation era, when due to reheating, the huge thermodynamic entropy of cosmic radiation was released. Prior to this, near the Planck time in the quantum spacetime nugget, thermodynamic and gravitational entropy were very small (Past Hypothesis) and (quantum-gravitationally) the info content could have been minimal too.

A still open question is the conjecture by some recent authors that the info bit is physical, ie is equivalent to a very small mass-energy. Quantum mechanical experiments seem to point in this direction: quantum Szilard engine, fluctuation theorem, reversible dynamics.
 
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That's pretty good. However, it is easy to stumble without a very good definition of information, and distinction between information, knowledge and entropy.

For a macro example, consider a 64GB hard disc. It holds 64GB of information if all the bits are zero, or all one, or if the disc stores a copy of the library of Congress. The information content is invariant. However, the Shannon information, depends entirely on the bit patterns. So there must be multiple definitions of information at play.

My PF Insights article delves into the many ways to define information in physics.
https://www.physicsforums.com/insights/how-to-better-define-information-in-physics/

Here's a difficult case: particle decay. How could we do an information balance on this? Information in equals information out.
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