  In the setting of the principle of local equilibrium which asserts that the
temperature is a function of the energy levels of the system, we exhibit plenty
of steady states describing the condensation of free Bosons which are not in
thermal equilibrium. The surprising facts are that the condensation can occur
both in dimension less than 3 in configuration space, and even in excited
energy levels. The investigation relative to non equilibrium suggests a new
approach to the condensation, which allows an unified analysis involving also
the condensation of $q$-particles, $-1\leq q\leq 1$, where $q=\pm1$ corresponds
to the Bose/Fermi alternative. For such $q$-particles, the condensation can
occur only if $0<q\leq1$, the case 1 corresponding to the standard
Bose-Einstein condensation. In this more general approach, completely new and
unexpected states exhibiting condensation phenomena naturally occur also in the
usual situation of equilibrium thermodynamics. The new approach proposed in the
present paper for the situation of $2^\text{nd}$ quantisation of free
particles, is naturally based on the theory of the Distributions, which might
hopefully be extended to more general cases
