Detailed balance says that the total probability of going from m to n in the stationary distribution, which is the probability of starting at m ρ ρ m times the probability of hopping from m to n, is equal to the probability of going from n to m, so that the total back-and-forth flow of probability in equilibrium is zero along any hop. The condition is automatically satisfied when n=m, so it has the same form when written as a condition for the transition-probability R matrix.