  Predictive statistical mechanics is a form of inference from available data,
without additional assumptions, for predicting reproducible phenomena. By
applying it to systems with Hamiltonian dynamics, a problem of predicting the
macroscopic time evolution of the system in the case of incomplete information
about the microscopic dynamics was considered. In the model of a closed
Hamiltonian system (i.e. system that can exchange energy but not particles with
the environment) that with the Liouville equation uses the concepts of
information theory, analysis was conducted of the loss of correlation between
the initial phase space paths and final microstates, and the related loss of
information about the state of the system. It is demonstrated that applying the
principle of maximum information entropy by maximizing the conditional
information entropy, subject to the constraint given by the Liouville equation
averaged over the phase space, leads to a definition of the rate of change of
entropy without any additional assumptions. In the subsequent paper
(http://arxiv.org/abs/1506.02625) this basic model is generalized further and
brought into direct connection with the results of nonequilibrium theory.
