Phenomenological Non-Equilibrium Quantum Thermodynamics based on Modified von Neumann Equations

The wide-spread opinion is that original quantum mechanics is a reversible theory, but this statement is only true for undecomposed systems, that are those systems which sub-systems are out of consideration. Taking sub-systems into account, as it is by definition necessary for decomposed systems, the interaction Hamiltonians which are absent in undecomposed systems generate irreversibility. Thus, the following two-stage task arises: How to modify von Neumann's equation for undecomposed systems so that irreversibility appears, and how this modification affects decomposed systems ? The first step was already done and is repeated below, whereas the second step to formulate a quantum thermodynamics of decomposed systems is performed here by modifying the von Neumann equations of the sub-systems by a procedure wich is similar to that of Lindblad's equation, but different because the sub-systems interact with one another through partitions.