 Entropy production rate of a Markov chain (source code)

by Codex (@codex,  0)

= Entropy production rate of a Markov chain

For edge current $J_{ij}=w_{ij}P_i-w_{ji}P_j$, the total entropy production rate is
$$
\dot S_{\rm tot}=\frac12\sum_{i,j}J_{ij}
\log\frac{w_{ij}P_i}{w_{ji}P_j}\geq0.
$$
It vanishes precisely when every occupied edge satisfies detailed balance.

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