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What is the relationship between Energy, Entropy, and Information?

I read this - What Is Energy? Where did it come from? - and the top answer says that 'energy' is an abstract number that is a property of nature that just so happens to be conserved because 'operations' on nature are symmetric in time (time-translational symmetry).

The other conservation law (I've heard) for an abstract number that is a property of nature is Information - as in 'Black holes must behave this way because otherwise they would violate conservation of information'. But I don't know why it's conserved.

The third abstract number that is a property of nature, but that does NOT obey conservation along the direction of time - 'Entropy'. Why isn't this conserved if the other two are?

How are these three related? Again I can't follow complex math, but these must be fundamentally related to each right?

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2 Answers 2

Entropy is a measure of the order/disorder during the transformation of the state of a system and is defined as the total variation of energy at defined temperature. From statistical mechanics point of view this variation of energy are generated from statistical transitions of the internal states of the system. In this sense the entropy can measure how is easy to reach a defined state of the system. Now imagine a text stream that arrive to you character by character in a screen. If the text is meaningless every character has the same probability to appears to you and then the entropy is maximal because this disorder is maximal. If you want transfer an information you have to spent a little of energy in ordering the characters because this do not happens spontaneously. The final state of the system is more ordered in respect the early one so the entropy is less of the entropy of random text. This means that if you want reduce entropy in order transfer information you must spent energy.

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that doesn't explain why entropy must increase with time –  James Kujareevanich Jul 5 '12 at 11:19
    
Entropy measure the total variation of energy. If the system is going on a more foundamental state loose a part of energy and entropy increase, on contrary entropy is diminished. –  Emanuele Luzio Jul 5 '12 at 13:02
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Entropy is not the total variation of energy at a defined temperature. The change in entropy is the heat flow divided by the temperature. If you squeeze a gas slowly, you increase the energy without increasing the entropy. –  Ron Maimon Jul 5 '12 at 15:46

I am going to address the question as to why energy and information have time symmetric conservation properties whereas entropy does not.

According to the Wikipedia entry on entropy - "The entropy of an isolated system never decreases, because isolated systems spontaneously evolve towards thermodynamic equilibrium, which is the state of maximum entropy."

Therefore, entropy will only increase with time in an isolated system if it has not reached thermodynamic equilibrium. The universe is an isolated system that had a very low entropy state in the past, i.e. at or shortly after the big bang. Therefore it is in the process of approaching thermodynamic equilibrium. Therefore it is a circumstance of the state of our universe that causes entropy to increase with time, at this time. It is not a law.

Conservation of energy and information are laws. Increasing entropy is a circumstance. That is why they are different.

I hope this helps. It’s hard to find straight answers to this question, which suggests that we really don’t know the answer yet.

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