The concept of the classical-like Wehrl entropy is shown to be a very
sensitive and informative measure describing the time evolution of a q
uantum system. Its applications to the Jaynes-Cummings model reveal re
levant aspects of the field dynamics. The Wehrl entropy provides a com
pact one-parameter description giving, among other things, a clear sig
nature for the splitting of the Q function. It gives also a clear indi
cation of the phase randomization of the coherent electromagnetic fiel
d states during the interaction with a two-level atom.