This paper presents the computational methods of information cohomology applied to genetic expression in [125,16,17] and in the companion paper [16] and proposes its interpretations in terms of statistical physics and machine learning. In order to further underline the Hochschild cohomological nature af information functions and chain rules, following [13,14,133], the computation of the cohomology in low degrees is detailed to show more directly that the k multivariate mutual-informations (I k ) are k-coboundaries. The k-cocycles condition corresponds to I k = 0, which generalize statistical independence to arbitrary dimension k [16]. Hence the cohomology can be interpreted as quantifying the statistical dependences and the obstruction to factorization. The topological approach allows to investigate Shannon's information in the multivariate case without the assumptions of independent identically distributed variables and of statistical interactions without mean field approximations. We develop the computationally tractable subcase of simplicial information cohomology represented by entropy H k and information I k landscapes and their respective paths. The I1 component defines a self-internal energy functional U k , and (−1) k I k,k≥2 components define the contribution to a free energy functional G k (the total correlation) of the k-body interactions. The set of information paths in simplicial structures is in bijection with the symmetric group and random processes, provides a trivial topological expression of the 2nd law of thermodynamic. The local minima of free-energy, related to conditional information negativity, and conditional independence, characterize a minimum free energy complex. This complex formalizes the minimum free-energy principle in topology, provides a definition of a complex system, and characterizes a multiplicity of local minima that quantifies the diversity observed in biology. I give an interpretation of this complex in terms of frustration in glass and of Van Der Walls k-body interactions for data points.