  We study generic matter coupled to a $D$-dimensional supergravity using a
formulation of Double Field Theory (DFT), where all the fields are encoded in
O$(D,D)$ multiplets. We study both the case when the matter comes from a
variational principle, as well as the case where the matter comes from a
statistical or thermodynamic approach. For the latter, we construct the
distribution function for the perfect fluid and its entropy current, which is a
conserved quantity. We then include general viscous and elastic terms in the
generalized energy-momentum tensor which, in the general case, lead to entropy
production. We consistently deform the conservation law of the generalized
entropy current and identify a particular non-dissipative deformation. Using
the generalized fluid model, we revisit the issue of non-covariance of perfect
fluids under T-dualities and we show how to resolve it in our DFT model with
matter.
