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## Information theory and renormalization group flows

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 entropy is an extensive

quantity and 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.