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What is the connectivity between Boltzmann's entropy expression and Shannon's entropy expression? mentions a realtionship between Shannon entropy and Bolltzmann entropy. Is there a relationship between Kolmogorov Sinai entropy and Boltzmann entropy? And kolmogorov entropy and Shannon entropy?

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Srishti M
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This is a contentious question depending on the researcher answering and their background. Much of the available literature on the subject(s) will say that although the forms of these equations are similar, there is no relation between Shannon and Boltzman entropy. The best treatment I've seen stems from E.T. Jaynes' classical paper on the subject and is presented by Arieh Ben-Naim in his book Farewell to Entropy.

Chris Aldrich
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  • I have come across the paper : Journal Article 2005 1424-9286 J Milan Journal of Mathematics 73 1

    "Some Remarks on the Definition of Boltzmann, Shannon and Kolmogorov Entropy"

    Birkhäuser-Verlag 2005-10-01

    by Benci, Vieri, A Menconi, Giulia pages 187-209 where they mention that the entropies can be represented by Boltzmann entropy. However, it is difficult to follow and as you mentioned there are contradictions and the topic is debatable. So what is the real answer/

     – Srishti M Feb 28 '14 at 19:22
  • "there is no relation between Shannon and Boltzman entropy", didn't you mean between Boltzman entropy and Kolmogrov entropy ? – loxaxs Apr 07 '18 at 05:55
  • Jayne's paper was published before Kolmogorov's, so this doesn't really answer the question – Ben H Nov 30 '22 at 18:21
  • I don't see what is contentious on the mathematical part of the questions, which i think is what the OP was interested in. Mathematically all the entropies are equal -under appropriate, natural assumption, where all are defined. Now if we consider the physics of such situations i guess there are subtleties which are what is discussed in physics. – plm Nov 01 '23 at 20:16