Investigation of an energy nonadditivity for nonextensive systems

We investigate the energy nonadditivity relationship E(A∪B) = E(A) + E(B) + αE(A)E(B) which is often considered in the development of the statistical physics of nonextensive systems. It was recently found that α in this equation was not constant for a given system in a given situation and could not characterize nonextensivity for that system. In this work, we select several typical nonextensive systems and compute the behavior of α when a system changes its size or is divided into subsystems in different fashions. Three kinds of interactions are considered. It is found by a thought experiment that α depends on the system size and the interaction as expected and on the way we divide the system. However, one of the major results of this work is that, for given system, α has a minimum with respect to division position. Around this position, there is a zone in which α is more or less constant, a situation where the sizes of the subsystems are comparable. The width of this zone depends on the interaction and on the system size. We conclude that if α is considered approximately constant in this zone, the two mathematical difficulties raised in previous studies are solved, meaning that the nonadditive relationship can characterize the nonadditivity of the system as an approximation. In all the cases, α tends to zero in the thermodynamic limit (N→∞) as expected.