Chaos and randomness: An equivalence proof of a generalized version of the Shannon entropy and the Kolmogorov–Sinai entropy for Hamiltonian dynamical systems | Roman Frigg - Academia.edu

Chaos is often explained in terms of random behaviour; and having positive Kolmogorov–Sinai entropy (KSE) istaken to be indicative of randomness. Although seemly plausible, the association of positive KSE with random behav-iour needs justification since the definition of the KSE does not make reference to any notion that is connected to ran-domness. A common way of justifying this use of the KSE is to draw parallels between the KSE and Shannon's information theoretic entropy. However, as it stands this no more than a heuristic point, because no rigorous connec-tion between the KSE and Shannon's entropy has been established yet. This paper fills this gap by proving that the KSEof a Hamiltonian dynamical system is equivalent to a generalized version of Shannon's information theoretic entropyunder certain plausible assumptions.