  The Boltzmann-Gibbs probability distribution, seen as a statistical model,
belongs to the exponential family. Recently, the latter concept has been
generalized. The q-exponential family has been shown to be relevant for the
statistical description of small isolated systems. Two main applications are
reviewed: 1. The distribution of the momentum of a single particle is a
q-Gaussian, the distribution of its velocity is a deformed Maxwellian; 2. The
configurational density distribution belongs to the q-exponential family. The
definition of the temperature of small isolated systems is discussed. It
depends on defining the thermodynamic entropy of a microcanonical ensemble in a
suitable manner. The simple example of non-interacting harmonic oscillators
shows that Renyi's entropy functional leads to acceptable results.
