Mutual information via thermodynamics: Three different approaches

Three different approaches to derive mutual information via thermodynamics are presented where the temperature-dependent energy is given by: (a) $β\mathcal{E} = -\ln[P(X,Y)]$, (b) $β\mathcal{E} =-\ln[P(Y|X)]$ or (c) $β\mathcal{E} =-\ln[P(X|Y)]$. All approaches require the extension of the traditional physical framework and the modification of the 2nd law of thermodynamics. A realization of a physical system with an effective temperature-dependent Hamiltonian is discussed followed by a suggestion of a physical information-heat engine.

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