Figure 3.

Time evolution of population probability P_A(t) as obtained from Eq. 2.7, starting from state A and assuming transition probabilities γ_ba=k_a=1∕10 and γ_ab=k_b=1∕20 for illustration. The system relaxes with a decay rate of γ_ab+γ_ab=3∕20 and approaches equilibrium, P_A(∞)=1−⟨N_B⟩_eq∕N=γ_ab∕(γ_ba+γ_ab)=1∕3, as expected. Also shown is the result of a dynamical Monte Carlo simulation (dotted line), which agrees well with the matrix multiplication method (solid line), when 10⁶ trajectories are employed.