  A mapping of nonextensive statistical mechanics into Gibbs' statistical
mechanics exists, which leads to a generalization of Einstein's formula for
fluctuations. A unified treatment of stability of relaxed states in
nonextensive statistical mechanics and Gibbs' statistical mechanics follows.
The former and the latter are endowed with probability distribution of
microstates ruled by power laws and Boltzmann exponentials respectively. We
apply our treatment to the relaxed states described by a 1D nonlinear
FokkerPlanck equation. If the latter is associated to the stochastic
differential equation obtained in the continuous limit from a 1D, autonomous,
discrete map affected by noise, then we may ascertain whether if a relaxed
state follow a power law distribution (and with which exponent) by looking at
both map dynamics and noise level, with no assumptions concerning the additive
or multiplicative nature of the noise and with no numerical computation of the
orbits. Results agree with the simulations of Sanchez et al. EPJ 143.1 (2007)
141-143 concerning relaxation to a Pareto-like distribution.
