  There is a consensus in science that information theory and statistical
physics have a close relationship but the literary proofs of the equivalence
between most of the conceptions in the two disciplines are still missing. In
this work, according to the statistical ensembles' description of the
information sequences that are generated by the i.i.d. single variable and
multivariate information source, the relationship between the ensemble
equivalence and asymptotic equipartition property is established. We find that
the description of information sequences in classical information theory is a
special case of the canonical ensemble description of information sequences.
They are both the maximum entropy approximation of the real signal generation.
Vice versa, the conjugate microcanonical ensemble description of the
information sequences under hard constraints satisfies the condition in real
signal generation exactly. Thus, the microcanoincal ensemble description is
closer to the real signal generation than the conjugate canonical ensemble, but
the ensemble equivalence between the microcanonical and canonical ensemble in
the thermodynamic limit guarantees the effectiveness of classical information
theory, i.e., the asymptotic equipartition property in information theory is an
isotope of ensemble equivalence from statistical physics.

Statistical Mechanics