  This article presents several results establishing connections be- tween
Markov chains and dynamical systems, from the point of view of open systems in
physics. We show how all Markov chains can be understood as the information on
one component that we get from a dynamical system on a product system, when
losing information on the other component. We show that passing from the
deterministic dynamics to the random one is character- ized by the loss of
algebra morphism property; it is also characterized by the loss of
reversibility. In the continuous time framework, we show that the solu- tions
of stochastic dierential equations are actually deterministic dynamical systems
on a particular product space. When losing the information on one component, we
recover the usual associated Markov semigroup.
