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If the von Neumann equation is modified by time dependent statistical weights, the time rate of entropy, the entropy exchange and the production of a Schottky system are derived whose Hamiltonian does not contain the interaction with the system’s environment. This interaction is semi-classically described by the quantum theoretical expressions of power and entropy exchange.

Concepts of Phenomenological Irreversible Quantum Thermodynamics I: Closed Undecomposed Schottky Systems in Semi-Classical Description