The book first considers that the evolution of quantum operators is canonical with the total Hamiltonian, and that the generator of the temporal evolution of the classical variables is the mean value of this Hamiltonian, evaluated with a purely quantum Density Matrix. The authors introduce the general MaxEnt Density Matrix for systems where quantum and classical degrees of freedom interact. This methodology can describe the interaction between microscopic and macroscopic degrees of freedom. Next, the objectivity of the mathematical description of electric charge transport is explored. It is shown that the description of electric charge transport using fractional order derivatives is non objective. Similarly, the closing study explores the mathematical description of mechanical movement.