visited set was $A$ are depicted in red, and those for which the last visited set was $B$ are depicted in black. []{data-label="fig:trajAB"}](fig2){width="3in"}

Based on this assignment, we can introduce the following quantities. If $N^T_{A,B}$ denotes the total number of times the trajectory went from being assigned to $A$ to being assigned to $B$ during the time interval $[0,T]$ (i.e. the number of times it switched from red to black in Fig. \[fig:trajAB\]), we set $$\label{eq:nuAB}
  \nu_R=\lim_{T\to\infty}  \frac{N^T_{A,B}}{T}.$$ This quantity gives the average frequency at which the trajectory goes from $A$ to $B$ which, because the system is at steady state, is also the same as the average frequency at which the trajectory goes from $B$ to $A$ since $N^T_{A,B} = N^T_{B,A}$ asymptotically. The rate in  is referred to as the rate of the reactive trajectories in TPT, hence the subscript $R$. The rate of reactive trajectories $\nu_R$ should not be confused with the two reaction rates from $A$ to $B$ and $B$ to $A$ defined respectively as $$\label{eq:kAB} 
  k_{A,B}= \lim_{T\to\infty} \frac{N^T_{A,B}}{T_A}, \quad 
  k_{B,A}= \lim_{T\to\infty} \frac{N^T_{A,B}}{T_B},$$ where $T_A$ and $T_B$ are, respectively, the total times during which the trajectory was assigned to $A$ or $B$ in the interval $[0,T]$ (i.e. 