Gibbs Paradox as Property of Observation, Proof of II. Principle of Thermodynamics

Our way to deal with the given topic is a connection of both the mathematical definitions of information entropies and their mutual relations within a system of stochastic quantities especially with thermodynamic entropies defined on an isolated system in which a realization of our (repeatable) observation is performed [it is a (cyclic) transformation of heat energy of an observed, measured system]. We use the information description to analyze Gibbs paradox reasoning it as a property of such observation, measuring of an (equilibrium) thermodynamic system. We state a logical proof of the II. P.T. as a derivation of relations among the entropies of a system of stochastic variables, realized physically, and, the Equivalence Principle of the I., II. and III. Principle of Thermodynamics is formulated.