  A path information is defined in connection with the different possible paths
of chaotic system moving in its phase space between two cells. On the basis of
the assumption that the paths are differentiated by their actions, we show that
the maximum path information leads to a path probability distribution as a
function of action from which the well known transition probability of Brownian
motion can be easily derived. An interesting result is that the most probable
paths are just the paths of least action. This suggests that the principle of
least action, in a probabilistic situation, is equivalent to the principle of
maximization of information or uncertainty associated with the probability
distribution.
