  A path information is defined in connection with the probability distribution
of paths of nonequilibrium hamiltonian systems moving in phase space from an
initial cell to different final cells. On the basis of the assumption that
these paths are physically characterized by their action, we show that the
maximum path information leads to an exponential probability distribution of
action which implies that the most probable paths are just the paths of
stationary action. We also show that the averaged (over initial conditions)
path information between an initial cell and all the possible final cells can
be related to the entropy change defined with natural invariant measures for
dynamical systems. Hence the principle of maximum path information suggests
maximum entropy and entropy change which, in other words, is just an
application of the action principle of classical mechanics to the cases of
stochastic or instable dynamics.
