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Physical entropies SB are defined with respect to a certain set of variables, the observationlevel B. For all times in which B exists, SB is the uncertainty H of a density operator RB making H a maximum with respect to the experimental values of B. This definition is not restricted to the thermodynamic equilibrium. The entropies SB measure the vagueness of the description in Hilbert-space caused by the choice of B. The time dependence of the density operator R B is not governed by the von Neumann equation, but in the special case of a “self-consistent“ B it may be calculated with the help of this equation. An increasing SB is obtained. If the times for which B exists are sufficiently close, a macroscopic equation for the time deriva· tive of SB is given. Three special cases of B are considered, leading to the Gibbs equation, a generalized entropy equation for heat conduction and an entropy equation for the multipole relaxation.
Helmut Schwegler (Wed,) studied this question.