  The superstatistics approach recently introduced by Beck [C. Beck and E.G.D.
Cohen, Physica A 322, 267 (2003)] is a formalism that aims to deal in a
unifying way with a large variety of complex nonequilibrium systems, for which
spatio-temporal fluctuations of one intensive variable (the "temperature" 1/b)
are supposed to exist. The intuitive explanation provided by Beck for
superstatistics is based on the ansatz that the system under consideration,
during its evolution, travels within its phase space which is partitioned into
cells. Within each cell, the system is described by ordinary Maxwell-Boltzmann
statistical mechanics, i.e., its statistical distribution is the canonical one,
but b varies from cell to cell, with its own probability density f(b). In this
work we first address that the explicit inclusion of the density of states in
this description is essential for its correctness. The correction is not
relevant for developments of the theory, but points to the fact that its
correct starting point, as well its meaning, must be found at a more basic
level: the pure probability product rule involving the intensive variable b and
its conjugate extensive one. The question therefore arises how to assign a
meaning to these probabilities for each specific problem. We will see that it
is easily answered through Bayesian analysis. This way, we are able to provide
an interpretation for f(b), that was not fully elucidated till now.

Statistical Mechanics