Statistical and kinematic arrangements and their thermodynamic and informational interpretations: Gibbs paradox

Abstract A new way to deal with the given topic is the approach of finding the connection between the mathematical definitions of statistical and information entropy, as well as their mutual relations within the system of stochastic quantities. Especially with thermodynamic entropies expressed on an isolated system in which our repeatable observations are made and where it is a cyclic conversion of thermal energy within the observed/measured system. At the same time, we use the description of information to analyze the Gibbs paradox, which is also a current property of such observation/measurement of an equilibrium thermodynamic system. Although not immediately obvious in the first connection with the thermal analysis, it indicates a whole series of questions not yet solved but greedy like this one.