  The nonextensive entropic measure proposed by Tsallis introduces a parameter,
q, which is not defined but rather must be determined. The value of q is
typically determined from a piece of data and then fixed over the range of
interest. On the other hand, from a phenomenological viewpoint, there are
instances in which q cannot be treated as a constant.
  We present two distinct approaches for determining q depending on the form of
the equations of constraint for the particular system. In the first case the
equations of constraint for an operator O can be written as $Tr[F^{q}O]=C$,
where C may be an explicit function of the distribution function, F. In this
case one can solve an equivalent MAXENT problem which yields q as a function of
the corresponding Lagrange Multiplier. As an illustration the exact solutions
to the static Generalized Fokker-Planck Equation (GFP) are obtained from
MAXENT. As in the case where C is a constant if q is treated as a variable
within the MAXENT framework, the entropic measure is maximized for all values
of q trivially. Therefore q must be determined from existing data. In the
second case an additional equation of constraint exists which cannot be brought
into the above form. In this case the additional equation of constraint may be
used to determine the fixed value of q.

Statistical Mechanics