N2 does not cause addiction, or dependence, in a physiological sense.
An uncomplicated definition of physiological addiction would be the persistent need for and use of a habit-forming substance characterized by tolerance and well-defined physical signs & symptoms upon withdrawal. [Tolerance: the markedly increased intake of the substance is needed to achieve the same effect or, with continued use, the same amount of the substance has markedly less effect.]
In general, the terms addiction or dependence refer to the compulsive use of a substance known to be harmful (e.g., heroin, nicotine or alcohol), although there are cases were they are the unwanted side effect of medical treatment. The long-term use of drugs prescribed to control severe pain, such as morphine, would be an example of the later situation.
N2 is inert & therefore cannot be habit-forming. While a diver may become more attuned to the effects of increased partial pressures of N2, i.e., nitrogen narcosis, and more adept at managing their potential adverse impact, tolerance in a physiological sense does not develop. Nor do bona fide withdrawal signs or symptoms. Finally, while N2 can be harmful in the sense that its improper elimination from the body may result in such things as DCS, I've never heard of a diver who engaged in persistent compulsive scuba when diving gave him the bends.
N2 probably does not cause addiction, or dependence, in a psychological sense, either.
One must appreciate that "psychological addictions" are produced by neurochemical mechanisms as well, and the distinction between physiological v psychic is not easy to draw, and ultimately may not be meaningful in a medical sense.
If you wish a contrasting definition, psychological addiction could be defined as a condition in which an activity produces a feeling of satisfaction & need that requires regular use in order to produce pleasure or to avoid discomfort (e.g., anxiety or depression).
I suppose that some divers may need periodic or continuous scuba to generate pleasure or avoid psychological pain, but I very much doubt that this is related to any effects of N2, e.g., narcosis. Rather, I suspect that it is based on the pleasure one derives from escaping from a pathological life situation to the many enjoyments of dive trips & scuba proper.
Interesting topic.
Best regards.
DocVikingo