I have an MD simulation that I'm pretty confident it works correctly. One of my tests was to check if the velocity distribution follows a Maxwell Boltzmann distribution.
As indicated, the simulated data match the theoretical curve. However, there is something I do not understand.
As I recall from my studies of statistical mechanics, the Maxwell Boltzmann distribution is a probability distribution for the speed of all particles in a system that has reached equilibrium.
In my case, I'm considering the velocities of only one particle since the beginning of simulation to its end. That is, I'm not looking at the speeds of all the particles, and I'm not waiting for the system to reach equilibrium. Yet, the data fits theory almost perfectly. What could be the explanation for my results? (The Wikipedia page defines the distribution as giving the probability of finding the particle near a speed $v$. Could it be that the distribution actually concerns one particle and I'm remembering it wrong?)