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Different dynamics of the non-equilibrium canonical density operator, such as Canonical Dynamics, Linear Projection Dynamics, Generalized Robertson Dynamics, and Contact Time Dynamics, especially for time dependent work variables are derived. For two discrete systems in contact the rate of entropy is non-negative, if the contact time is short, and if one of the two discrete systems is in equilibrium and the compound system composed of both is isolated. The contact temperature is identified with one of the Lagrange parameters of the non-equilibrium canonical density operator of the compound system.

Different Dynamics and Entropy Rates in Quantum-Thermodynamics