Dynamic entropy as a measure of caging and persistent particle motion in supercooled liquids

The length-scale dependence of the dynamic entropy is studied in a molecula r dynamics simulation of a binary Lennard-Jones liquid above the mode-coupl ing critical temperature T-c. A number of methods exist for estimating the entropy of dynamical systems, and we utilize an approximation based on calc ulating the mean first-passage time (MFPT) for particle displacement becaus e of its tractability and its accessibility in real and simulation measurem ents. The MFPT dynamic entropy S(epsilon) is defined as equal to the invers e of the average first-passage time for a particle to exit a sphere of radi us epsilon. This measure of the degree of chaotic motion allows us to ident ify characteristic time and space scales and to quantify the increasingly c orrelated particle motion and intermittency occurring in supercooled liquid s. In particular, we identify a "cage" size defining the scale at which the particles are transiently localized, and we observe persistent particle mo tion at intermediate length scales beyond the scale where caging occurs. Fu rthermore, we find that the dynamic entropy at the scale of one interpartic le spacing extrapolates to zero as the mode-coupling temperature T-c is app roached. [S1063-651X(99)00711-4].