At stationarity,
$$
\alpha P_1^{\rm ss}=\frac{\alpha\beta}{\alpha+\beta}
=\beta P_2^{\rm ss}.
$$
Thus every edge current vanishes and the two-state system satisfies <detailed balance>. A network containing only one undirected edge cannot sustain a stationary cycle current.

Solution

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

 Solution

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