# Information Theory and Entropy

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• Arman777
CPT seems to imply it. You can reverse the system evolution by applying charge, parity and time conjugation, so the information about the past must be contained in the present state. That implies conservation of information by the evolution.f

#### Arman777

Gold Member
1-Whats the relationship between entropy and İnformation ?
2-Can Entrophy always increases statement imply information lost ?
3-If it implies how its lost ?

1. Entropy and information are basically opposites. Entropy tells you how many quantum states are consistent with the information you have. If you have more information about the state, then there are fewer states that match the description, so the entropy is less.
2. Yes.
3. When two particles interact, they trade some energy and momentum. The amount of energy/momentum transfer is in superposition. Somehow, the wavefunction collapses, and the amount of transfer takes on some random value. So, if we initially knew the energy/momentum of each particle before the interaction, afterwards we only know the total. So some information was lost. It's not clear how this wavefunction collapse occurs.

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Arman777
1. Entropy and information are basically opposites. Entropy tells you how many quantum states are consistent with the information you have. If you have more information about the state, then there are fewer states that match the description, so the entropy is less.
2. Yes.
3. When two particles interact, they trade some energy and momentum. The amount of energy/momentum transfer is in superposition. Somehow, the wavefunction collapses, and the amount of transfer takes on some random value. So, if we initially knew the energy/momentum of each particle before the interaction, afterwards we only know the total. So some information was lost. It's not clear how this wavefunction collapse occurs.

I understand thanks, "So some information was lost" , I remembered now that I heard İnformation never lost, never vanishes. Is this true ?
Like Conservation of Information ?

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I searched a bit and says there's no such conservation but From unitarity or cpt there could be
"CPT seems to imply it. You can reverse the system evolution by applying charge, parity and time conjugation, so the information about the past must be contained in the present state. That implies conservation of information by the evolution.

This may not be the answer you wanted, because it does not imply unitarity, but it is the only relationship between symmetry and information conservation that I can think of. Unitarity seems to be a very fundamental assumption though, and there is not much more fundamental mathematical structure you could use to argue about its necessity." (A.O.Tell,Physics Stack Exchange,https://physics.stackexchange.com/q...associated-to-the-conservation-of-information)

But, wavefunction collapse is not a unitary transformation.

But, wavefunction collapse is not a unitary transformation.
I don't know much things about wavefunction actually I am freshman at physics :)
So it doesn't conserved.
Like energy,momentum etc is even not conserved in macroscopic states,like galaxy clusters scale etc.So It make sense to me that its not conserved.Maybe we can say the information about the system is lost during the time.It never disappeares but it just turns something that we can't describe the full system after a period of time using previous information

I searched a bit and says there's no such conservation but From unitarity or cpt there could be
"CPT seems to imply it. You can reverse the system evolution by applying charge, parity and time conjugation, so the information about the past must be contained in the present state. That implies conservation of information by the evolution.
/QUOTE]

Sure, that's fine if it doesn't interact with anything.

Makes sense...

Well I read the article and says information is conserved.It can not be copied or lost.Which Complementarity came from that.