  First we describe briefly an information-action method for the study of
stochastic dynamics of hamiltonian systems perturbed by thermal noise and
chaotic instability. It is shown that, for the ensemble of possible paths
between two configuration points, the action principle acquires a statistical
form $<\delta A>=0$. The main objective of this paper is to prove that, via
this information-action description, some quantum like uncertainty relations
such as $<\Delta A>\geq\frac{1}{\sqrt{2}\eta}$ for action, $<\Delta x><\Delta
P>\geq\frac{1}{\eta}$ for position and momentum, and $<\Delta H><\Delta
t>\geq\frac{1}{\sqrt{2}\eta}$ for hamiltonian and time, can arise for
stochastic dynamics of classical hamiltonian systems. A corresponding
commutation relation can also be found. These relations describe, through
action or its conjugate variables, the fluctuation of stochastic dynamics due
to random perturbation characterized by the parameter $\eta$.
