  There remains a useful relation between diffusion and mobility for a Langevin
particle in a periodic medium subject to nonconservative forces. The usual
fluctuation-dissipation relation easily gets modified and the mobility matrix
is no longer proportional to the diffusion matrix, with a correction term
depending explicitly on the (nonequilibrium) forces. We discuss this correction
by considering various simple examples and we visualize the various
dependencies on the applied forcing and on the time by means of simulations.
For example, in all cases the diffusion depends on the external forcing more
strongly than does the mobility. We also give an explicit decomposition of the
symmetrized mobility matrix as the difference between two positive matrices,
one involving the diffusion matrix, the other force--force correlations.
