  The paper moves a step towards the full integration of statistical mechanics
and information theory. Starting from the assumption that the thermodynamical
system is composed by particles whose quantized energies can be modelled as
independent and identically distributed random variables, the paper proposes an
approach whose cornerstones are the information-theoretic typical set and the
conditional equiprobability of microstates given certain macrostates of the
system. When taken together, these two concepts explain why the standard
assumption of equally probable microstates is non-necessary (if not misleading)
and show that the celebrated Boltzmann-Planck entropy is indeed a conditional
entropy with deterministic condition. Several new specific results of physical
relevance are derived from this approach, among which are the probability
distribution of the occupancy numbers of the energy levels and an exact formula
for the ideal gas in a container that gives the entropy of the gas also at low
temperature. These specific results are pieces of a self-consistent and unified
framework that encompasses the cases of low and high temperature, of indexed
and non-indexed particles, of small and large number of particles, of
microcanonical, canonical and grand canonical ensembles.
