Mutual information via thermodynamics: Three different approaches

Three different approaches for deriving mutual information via thermodynamics are presented, where the temperature-dependent energy is given by (a) βε = ?ln[P(X, Y )], (b) βε = ?ln[P(Y |X)] or (c) βε = ?ln[P(X|Y )]. All approaches require the extension of the traditional physical framework and the modification of the second law of thermodynamics. A realization of a physical system with an effective temperature-dependent Hamiltonian is discussed and followed by a suggestion of a physical informationheat engine.