  The length-scale dependence of the dynamic entropy is studied in a molecular
dynamics simulation of a binary Lennard-Jones liquid above the mode-coupling
critical temperature $T_c$. A number of methods exist for estimating the
entropy of dynamical systems and we utilize an approximation based on
calculating the mean first-passage time (MFPT) for particle displacement
because of its tractability and its accessibility in real and simulation
measurements. The MFPT dynamic entropy $S(\epsilon)$ is defined to equal the
inverse of the average first-passage time for a particle to exit a sphere of
radius $\epsilon$. This measure of the degree of chaotic motion allows us to
identify characteristic time and space scales and to quantify the increasingly
correlated particle motion and intermittency occurring in supercooled liquids.
In particular, we identify a ``cage'' size defining the scale at which the
particles are transiently localized, and we observe persistent particle motion
at intermediate length scales beyond the scale where caging occurs.
Furthermore, we find that the dynamic entropy at the scale of one interparticle
spacing extrapolates to zero as the mode-coupling temperature $T_c$ is
approached.
