The basic principles of irreversible thermodynamics in the context of an informational-statistical approach

We consider on the light of Information Statistical Thermodynamics the basic principles of phenomenological thermodynamic theories, namely, the principles of equipresence, objectivity, and memory, as well as, the characteristics of entropy production. Informational Statistical Thermodynamics arises as a particular application of maximum-information-entropy inference. We discuss how in this perspective, together with the property of contraction of description based on Bogoliubov's hierarchy of relaxation times, it is possible to account for the above-mentioned principles. Particular analyses are carried out on the basis of a model system. Moreover, selecting the basic set of thermodynamical variables in a closed and in truncated approaches, we assess the validity of the approximations. In particular, we derive the limiting conditions under which one recovers the constitutive equations of Linear Irreversible Thermodynamics. The associated equations of evolution for the basic macrovariables and a particular H-theorem are described and discussed.