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We present a possible extension of the usual relativistic nuclear mean fieldmodels widely used to describe nuclear matter towards accounting for theinfluence of possible intrinsic fluctuations caused by the environment. Ratherthan individually identifying their particular causes we concentrate on thefact that such effects can be summarily incorporated in the changing of thestatistical background used, from the usual (extensive) Boltzman-Gibbs one tothe nonextensive taken in the form proposed by Tsallis with a dimensionlessnonextensivity parameter $q$ responsible for the above mentioned effects (for$q \rightarrow 1$ one recovers the usual BG case). We illustrate thisproposition on the example of the QCD-based Nambu - Jona-Lasinio (NJL) model ofa many-body field theory describing the behavior of strongly interacting matterpresenting its nonextensive version. We check the sensitivity of the usual NJLmodel to a departure from the BG scenario expressed by the value of $| q - 1|$,in particular in the vicinity of critical points.

Nonextensive critical effects in relativistic nuclear mean field models