“…In the above equation k B is the Boltzmann constant, T is the temperature, μ ( q⃗ ) is the spatially dependent mobility of the ligand molecule, and denotes either the potential affecting the ligand or the potential energy of the system in configuration given with q⃗ ;∇ q⃗ denotes the gradient with respect to the components of q⃗ . Introducing the survival probability function, S ( q⃗ o , t ), i.e., the probability that the ligand molecule located initially at q⃗ o has not yet reacted at time t : where P ( q⃗ , t | q⃗ o ,0) is the conditional probability that if the ligand molecule was at q⃗ o at time 0 then it will be at q⃗ at time t , resulting from the solution of the Smoluchowski eq , and the integration is over the whole volume V of the domain enclosed between δω and δΩ , one may evaluate the time τ( q⃗ o ) of the receptor–ligand association (the mean first-passage time ,, ) as We assume that for t < 0 the studied system is nonreactive, i.e., both δω and δΩ are reflective, and only an activation (or triggering) at t = 0 makes the association between the ligand and the receptor possible, such a situation is usually encountered in experiments involving pump–probe techniques. − Before the activation, the probability of finding the ligand at q⃗ o follows the equilibrium distribution P eq ( q⃗ o ) and thus the average time for association, τ, (or the global first-passage time) can be evaluated by integrating out the dependence of the mean first-passage time (eq ) on the initial position of the ligand: Again, the integration is over the whole volume V of the domain enclosed between δω and δΩ .…”