  We derive an exact equation governing two-particle backwards mean-squared
dispersion for both deterministic and stochastic tracer particles in turbulent
flows. For the deterministic trajectories, we probe the consequences of our
formula for short times and arrive at approximate expressions for the
mean-squared dispersion which involve second order structure functions of the
velocity and acceleration fields. For the stochastic trajectories, we
analytically compute an exact $t^3$ contribution to the squared separation of
stochastic paths. We argue that this contribution appears also for
deterministic paths at long times and present direct numerical simulation
results for incompressible Navier-Stokes flows to support this claim. We also
numerically compute the probability distribution of particle separations for
the deterministic paths and the stochastic paths and show their strong
self-similar nature.
