 Entropy production rate of a Markov chain

ID: 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}_{tot} = \frac{1}{2} \sum_{i, j} J_{ij} lo g \frac{w _{ij} P _{i}}{w _{ji} P _{j}} \geq 0.

It vanishes precisely when every occupied edge satisfies detailed balance.

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