  We theoretically study Langevin systems with a tilted periodic potential. It
has been known that the ratio $\Theta$ of the diffusion constant to the
differential mobility is not equal to the temperature of the environment
(multiplied by the Boltzmann constant), except in the linear response regime,
where the fluctuation dissipation theorem holds. In order to elucidate the
physical meaning of $\Theta$ far from equilibrium, we analyze a modulated
system with a slowly varying potential. We derive a large scale description of
the probability density for the modulated system by use of a perturbation
method. The expressions we obtain show that $\Theta$ plays the role of the
temperature in the large scale description of the system and that $\Theta$ can
be determined directly in experiments, without measurements of the diffusion
constant and the differential mobility.
