We investigate the nature of the effective dynamics and statistical forces obtained after integrating out nonequilibrium degrees of freedom. To be explicit, we consider the Rouse model for the conformational dynamics of an ideal polymer chain subject
to steady driving. We compute the effective dynamics for one of the many monomers by integrating out the rest of the chain. The result is a generalized Langevin dynamics for which we give the memory and noise kernels and the effective force, and we discuss the inherited nonequilibrium aspects.
We study the origin of buoyancy forces acting on a larger particle moving in a granular medium subject to horizontal shaking and its corrections before fluidization. In the fluid limit Archimedes law is verified; before the limit memory effects count
eract buoyancy, as also found experimentally. The origin of the friction is an excluded volume effect between active particles, which we study more exactly for a random walker in a random environment. The same excluded volume effect is also responsible for the mutual attraction between bodies moving in the granular medium. Our theoretical modeling proceeds via an asymmetric exclusion process, i.e., via a dissipative lattice gas dynamics simulating the position degrees of freedom of a low density granular sea.
