Oscillatory solutions of the rate equations. J. Fletcher in Phys. Lett. A 27:721 (1968).  What the paper says!?

This is a short (one page on two) paper which shows that rate equations whose relaxation rates are given by the detailed balance of thermal equilibrium, i.e., $$P_{i\to j}=P_{j\to i}\exp(-E_i/E_j)$$ relax towards their steady state without oscillations.

This shows that if there are oscillations, e.g., as in the case of J. Premanand, then the system is not excited around a thermal equilibrium:

The proof is simple and consists in including the constrain on the decay rates in the matrix so as to make manifest its real symmetric nature and thus with real eigenvalues.