Descripción: An information theory description of finite systems explicitly evolving in time is presented. We impose a MaxEnt variational principle on the Shannon entropy at a given time while the constraints are set at a former time. The resulting density matrix contains explicit time odd components in the form of collective flows. As a specific application we consider the dynamics of the expansion in connection with heavy ion experiments. Lattice gas and classical molecular dynamics simulations are shown. © 2007 American Institute of Physics.