  We present a derivation of power law canonical distributions from first
principle statistical mechanics, including the exponential distribution as a It
is presented a derivation of power law canonical distributions from first
principle statistical mechanics, including the exponential distribution as a
particular case. It is shown that these distributions arise naturally, and that
the heat capacity of the heat bath is the condition that determines its type.
As a consequence, it is given a physical interpretation for the parameter $q$
of the generalized entropy.
