  We discuss how to derive a Langevin equation (LE) in non standard systems,
i.e. when the kinetic part of the Hamiltonian is not the usual quadratic
function. This generalization allows to consider also cases with negative
absolute temperature. We first give some phenomenological arguments suggesting
the shape of the viscous drift, replacing the usual linear viscous damping, and
its relation with the diffusion coefficient modulating the white noise term. As
a second step, we implement a procedure to reconstruct the drift and the
diffusion term of the LE from the time-series of the momentum of a heavy
particle embedded in a large Hamiltonian system. The results of our
reconstruction are in good agreement with the phenomenological arguments.
Applying the method to systems with negative temperature, we can observe that
also in this case there is a suitable Langevin equation, obtained with a
precise protocol, able to reproduce in a proper way the statistical features of
the slow variables. In other words, even in this context, systems with negative
temperature do not show any pathology.
