  The Lorentz gas of $\mathbb{Z}^2$-periodic scatterers (or the so called Sinai
billiards) can be used to model motion of electrons on an ionized medal. We
investigate the linear response for the system under various external forces
(during both the flight and the collision). We give some characterizations
under which the forced system is time-reversible, and derive an estimate of the
electrical current generated by the forced system. Moreover, applying Pesin
entropy formula and Young dimension formula, we get several characterizations
of the non-equilibrium steady state of the forced system.
