I guess you could talk about the (Kolmogorov) complexity of a given string, versus the entropy of a dynamical system, but the two notions amount to the same thing if the string is generated by the system, as explained here. There is always the possibility that you flip a fair coin 100 times and it lands on Heads each time, thus producing a string with a short description, but the point is that this is unlikely.
ETA this is a purely mathematical statement and has nothing to do with physical entropy specifically.