  We formulate a geometric framework that allows to study momentum and energy
transport in non-relativistic systems. It amounts to coupling of the
non-relativistic system to the Newton-Cartan geometry with torsion. The
approach generalizes the classic Luttinger's formulation of thermal transport.
In particular, we clarify the geometric meaning of the fields conjugated to
energy and energy current. These fields describe the geometric background with
non-vanishing temporal torsion. We use the developed formalism to construct the
equilibrium partition function of a non-relativistic system coupled to the NC
geometry in 2+1 dimensions and to derive various thermodynamic relations
