Higher time derivatives of the generalized entropy

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Abstract
Using the generalized N‐body expression for a Liapunov functional developed by Prigogine, George, and Henin, a condition is obtained whereby the successive time derivatives of this functional alternate in sign for weakly coupled systems. This condition is applied and seen to hold true for generalized Bose and Fermi systems. An N‐body entropy is defined in terms of this functional, which contains diagonal as well as off‐diagonal elements of the density matrix. This ’’generalized entropy’’ is seen to be concave close to equilibrium, similar to the results of Harris. It does not appear that this property holds for the entropy far from equilibrium.