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I am interested to know if Kolmogorov Sinai Entropy of a system also known as Kolmogorov Complexity in information theory or popularly known as metric entropy increases with increase in dynamical noise. The dynamical noise can be in the form of deterministic chaotic noise. Consider, a linear system like an Auto Regressive (AR) model that is perturbed with chaotic noise. Will the entropy (Kolmogorov Sinai) of the output of the AR model increase? Intuitively, any kind of entropy increases with presence of noise. I am unable to find a proof or any relationship (preferably in literature or books) which have a relationship between entropy and noise. Can somebody please provide any guidelines as to how I should proceed to show that reduction in chaotic noise means decrease in Kolmogorov Sinai entropy and vice versa? Thank you

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