  In this paper a one-dimensional model of two infinite gases separated by a
movable heavy piston is considered. The non-linear Langevin equation for the
motion of the piston is derived from first principles for the case when the
thermodynamic parameters and/or the molecular masses of gas particles on left
and right sides of the piston are different. Microscopic expressions involving
time correlation functions of the force between bath particles and the piston
are obtained for all parameters appearing in the non-linear Langevin equation.
It is demonstrated that the equation has stationary solutions corresponding to
directional fluctuation-induced drift in the absence of systematic forces. In
the case of ideal gases interacting with the piston via a quadratic repulsive
potential, the model is exactly solvable and explicit expressions for the
kinetic coefficients in the non-linear Langevin equation are derived. The
transient solution of the non-linear Langevin equation is analyzed
perturbatively and it is demonstrated that previously obtained results for
systems with the hard-wall interaction are recovered.
