Can pairs of different physical systems be symmetrical under a process which would turn one of these physical system's entropic and informational contents into another system's respective informational and entropic contents — i. e.: one system's entropy is the other's information and vice versa — just like certain physical systems can be related by charge conjugation, parity transformation, and time reversal? What would one such pair of systems related by such an operation as 'entropy-information conjugation,' or whatever such an operation might be called, look like?

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    $\begingroup$ "one system's energy is the other's information" Energy and information are very different things, like motion and story. There is no real process that changes one into another. $\endgroup$ – Ján Lalinský Oct 10 '14 at 20:42
  • $\begingroup$ Energy is always conserved, both in Hamiltonian theory and in thermodynamics. Entropy (and information), on the other hand, are either not defined in Hamiltonian systems or they are not conserved in thermodynamics, so it's hard to see what kind of symmetry operation could exchange a conserved quantity against a non-conserved one. $\endgroup$ – CuriousOne Oct 10 '14 at 21:28
  • $\begingroup$ Sorry, I meant 'one system's entropy is the other's information;' I'll go back and fix that right now. $\endgroup$ – RandomDSdevel Oct 11 '14 at 19:45
  • $\begingroup$ The definition that I know for physical information is that it is identified with thermodynamic entropy through statistical physics. This makes your question trivial. What is your definition of information? $\endgroup$ – Steven Mathey Oct 11 '14 at 20:27
  • $\begingroup$ That sounds about right, but it seems to me that information is really information that is known about a system while entropy is really just a measure of how much information is not known about a system. What I'm curious about is this: what would change about a physical system if one could learn its unknown information and forget its known information — i. e.: what physical system would the information measured by another physical system's entropy generate? I'm assuming here that the fact that both information and entropy are measured in bits might let somebody find out… $\endgroup$ – RandomDSdevel Oct 11 '14 at 20:58

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