Indistinguishability of particles or independence of the random variables? (Q1368801)

Elementary facts are given around the basics of entropy and information (for discrete and continuous probability measures), on Sanov's theorem, the maximum probability principle and approaches to their solution. Connections to physical models (the distributions of Boltzmann and Gibbs, Planck-Bose-Einstein and Fermi-Dirac) are stressed. The formulae are kept elementary, no precise statement or proof is given.