So how does one calculate the entropy of a Markov Chain? Is it actually specified? If so, it seems buried.
The Markov chain provided as an example has the edge labels swapped (np should be qp and qp should be np). Regardless, what is the entropy of the example provided?
The problem with Markov chains is that states are dependent, so simply cataloguing states now violates the basic entropy calculation as neighboring states are now dependent on each other.
If the Markov chain is ergodic then maybe you can talk about the entropy of the stationary distribution? Then it's just $-\sum p_i lg(p_i)$ of the stationary distribution probabilities?
The article alludes to how entropy evolves. In the context of ergodic Markov chains, this is related to the size of the second eigenvalue?
So how does one calculate the entropy of a Markov Chain? Is it actually specified? If so, it seems buried.
The Markov chain provided as an example has the edge labels swapped (np should be qp and qp should be np). Regardless, what is the entropy of the example provided?
The problem with Markov chains is that states are dependent, so simply cataloguing states now violates the basic entropy calculation as neighboring states are now dependent on each other.
If the Markov chain is ergodic then maybe you can talk about the entropy of the stationary distribution? Then it's just $-\sum p_i lg(p_i)$ of the stationary distribution probabilities?
The article alludes to how entropy evolves. In the context of ergodic Markov chains, this is related to the size of the second eigenvalue?
[delayed]
Stochastic thermodynamics covers this
This predates stochastic thermo quite a bit. Entropy of markov chain is at least 50 y/o, maybe more.