  Finite-size effects are challenging in molecular dynamics simulations because
they have significant effects on computed static and dynamic properties, in
particular diffusion constants, friction coefficients and time- or
frequency-dependent response functions. We investigate the influence of
periodic boundary conditions on the velocity autocorrelation function and the
frequency-dependent friction of a particle in a fluid and show that the
long-time behavior (starting at the picosecond timescale) is significantly
affected. We develop an analytical correction allowing to subtract the periodic
boundary condition effects. By this we unmask the power-law long-time tails of
the memory kernel and the velocity autocorrelation function in liquid water and
a Lennard-Jones fluid from rather small simulation boxes.
