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

At stationarity $P_i=1/3$, but the cycle current is $J_i=(\alpha -\beta )/3$. Therefore the chain is out of detailed balance exactly whenThe nonzero cycle affinity $3\log (\alpha /\beta )$ sustains the stationary current and positive housekeeping entropy production.