Is it possible to calculate Shanon entropy for standard Markov chain?

04 September 2022 1 2K Report

Shanon entropy rate can be calculated for the hidden markov model (HMM) but is it possible to do the same for Markov chain.

Bryan Gorman

If it's finite, ergodic, and stationary, then yes, a Markov chain has an entropy (rate) that is the average information gained in one step. If H(i) is the entropy associated with all transitions outward from State i taken in one step, then the Markov chain entropy rate is is Sum(i) of P(i)H(i), where P(i) is the stationary probability of State i.

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