  This article extends the non-extensive entropy of Tsallis and uses this
entropy to model an energy producing system in an absorbing heat bath. This
modified non-extensive entropy is superficially identical to the one proposed
by Tsallis, but also incorporates a ''hidden'' parameter that provides greater
flexibility for modeling energy constraints. This modified non-extensive
entropy also leads to a more generalized family of energy transformation
functions and also exhibits the structural scale invariance properties
described in a previous article. This energy transformation also provides a
more natural mechanism by which arbitrary power-law distributions can be stated
in exponential form.
