Proposal of an Extension of Negentropy by Kullback-Leibler Information : 3rd Report, Cross Term and Mutual Negentropy
Negentropy should be defined by Kullback-Leibler information in a general situation, not by the difference of entropies nor by minus the entropy. In the present report, the formula of the negentropy defined by Kullback-Leibler information is expanded into some terms from two different viewpoints. Of the two expansions of this formula, one is done if accordance with the change of circumstances to which the system is exposed. The cross term of negentropy is derived from this expansion, and it represents the negentropy which is taken out of the system by replacing circumstances. The cross term of negentropy does not appear unless negentropy is defined by Kullback-Leibler information. The other expansion of the negentropy defined by Kullback-Leibler information is done in accordance with the division of a system into two subsystems. The mutual negentropy is derived from this expansion, and it represents the nonequilibrium between the two subsystems.
- Bulletin of JSME
Bulletin of JSME 29(257), 3795-3802, 1986