Different dynamics and entropy rates in quantum-thermodynamics

Different dynamics of the non-equilibrium canonical density operator, such as Canonical Dynamics, Linear Projection Dynamics, Generalized Robertson Dy namics, and Contact Time Dynamics, especially for time dependent work varia bles are derived. For two discrete systems in contact the rate of entropy i s non-negative, if the contact time is short, and if one of the two discret e systems is in equilibrium and the compound system composed of both is iso lated. The contact temperature is identified with one of the Lagrange param eters of the non-equilibrium canonical density operator of the compound sys tem.