Why is this a big deal? Most of the equations in physics that govern time evolution of particles obey time-reversal symmetry; the same differential equations that govern molecular or planetary motion will take you back to your starting point if you suddenly reverse the time variable. This is a usually a fantastic way to check to see if you are doing the physics correctly in your simulations, and also means that collections of starting points that are related to each other behave in certain predictable ways when they evolve.
If we have access to a time-reversible pseudo-random number generator, however, we get that very powerful tool back in our toolbox.
Now, the Langevin equation,
has two things that prevent it from being time-reversible. Besides the stochastic or random force, R(t), there’s also a drag or friction force, −γ(t)dxdt, that depends on the velocities of the particles. There’s no solution yet to time reversibility for this piece (and I have my doubts that there ever will be a way to reverse this).