  The thermodynamic equilibrium conditions for compact structures composed by
mass varying particles are discussed assuming that the so-called dynamical mass
behaves like an additional extensive thermodynamic degree of freedom. It then
follows that, such weakly interacting massive particles can form clusters of
non-baryonic matter or even astrophysical objects that, at cosmological scales,
are held together by gravity and by the attractive force mediated by a
background scalar field. The equilibrium conditions for resultant static,
spherically symmetric objects of uniform energy density are derived for the
case where the particles share essential features with the mass varying
mechanism in the context of cosmological scenarios. Physical solutions which
result in stable astrophysical lumps are obtained and discussed.
