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Continuous-time Markov chain

Master equation

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.


Entropy production rate of a Markov chain

Past exam of the mathematics course of the University of Cambridge / 2022 / iii / Paper 356 / 1 / a / Solution

Entropy production rate of a Markov chain

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