Decomposition of force fluctuations far from equilibrium

By studying a nonequilibrium Langevin system, we find that a simple condition determines the decomposition of the coarse-grained force into a dissipative force, an effective driving force and noise. From this condition, we derive a universal inequality, $D⩾\gamma {\mu }_{\mathrm{d}}^{2}T$, relating the diffusion constant $D$, the differential mobility ${\mu }_{\mathrm{d}}$, the bare friction constant $\gamma$ and the temperature $T$. Due to the general nature of the argument we present, we believe that our idea concerning this decomposition can be applied to a wide class of systems far from equilibrium.