  We present a possible approach to the study of the renormalization group (RG)
flow based entirely on the information theory. The average information loss
under a single step of Wilsonian RG transformation is evaluated as a
conditional entropy of the fast variables, which are integrated out, when the
slow ones are held fixed. Its positivity results in the monotonic decrease of
the informational entropy under renormalization. This, however, does not
necessarily imply the irreversibility of the RG flow, because the entropy
explicitly depends on the total number of degrees of freedom, which is reduced.
Only some size-independent additive part of the entropy could possibly provide
the required Lyapunov function. We also introduce a mutual information of fast
and slow variables as probably a more adequate quantity to represent the
changes in the system under renormalization and evaluate it for some simple
systems. It is shown that for certain real space decimation transformations the
positivity of the mutual information directly leads to the monotonic growth of
the entropy per lattice site along the RG flow and hence to its
irreversibility.
