What is the entropy of the quantum state vacuum in inflationary theory

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Consider the vacuum state that is hypothesised to precede the moment of inflation in classical inflationary theory.

The theory assumes that quantum fluctuations in this vacuum are magnified because of the process of inflation and have gone on to form the real energy structures that we witness in our present universe.

Obviously, these structures contain information and have therefore a degree of entropy. Since these structures can be ultimately traced back to the vacuum, is it reasonable to assume that the vacuum state must also possesses some kind of entropy?

If so, would one describe this entropy as low (perhaps considering the many quantum fluctuations to be information) or high (maybe since there is no real energy present in the vacuum)? Or can the vacuum be said not to have any entropy at all?
 
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The answer to this question is not straightforward. It depends on how one defines entropy. Generally speaking, entropy is a measure of disorder or uncertainty in a system. In the context of a vacuum state, it could be argued that there is some degree of entropy present. After all, the vacuum state is characterized by quantum fluctuations, which are unpredictable and random. However, since there is no energy present in the vacuum state, it could also be argued that the entropy is effectively zero. Ultimately, the answer to this question depends on one's definition of entropy and how much weight is given to the presence of quantum fluctuations.
 
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If we release an electron around a positively charged sphere, the initial state of electron is a linear combination of Hydrogen-like states. According to quantum mechanics, evolution of time would not change this initial state because the potential is time independent. However, classically we expect the electron to collide with the sphere. So, it seems that the quantum and classics predict different behaviours!
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