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 when
$$
\boxed{\alpha\ne\beta.}
$$
The nonzero cycle affinity $3\log(\alpha/\beta)$ sustains the stationary current and positive housekeeping entropy production.


Solution

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

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2022/iii/paper-356/1/h/solution