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In this paper a one-dimensional model of two infinite gases separated by amovable heavy piston is considered. The non-linear Langevin equation for themotion of the piston is derived from first principles for the case when thethermodynamic parameters and/or the molecular masses of gas particles on leftand right sides of the piston are different. Microscopic expressions involvingtime correlation functions of the force between bath particles and the pistonare obtained for all parameters appearing in the non-linear Langevin equation.It is demonstrated that the equation has stationary solutions corresponding todirectional fluctuation-induced drift in the absence of systematic forces. Inthe case of ideal gases interacting with the piston via a quadratic repulsivepotential, the model is exactly solvable and explicit expressions for thekinetic coefficients in the non-linear Langevin equation are derived. Thetransient solution of the non-linear Langevin equation is analyzedperturbatively and it is demonstrated that previously obtained results forsystems with the hard-wall interaction are recovered.Comment: 10 pages. To appear in Phys. Rev.

Langevin equation for the extended Rayleigh model with an asymmetric bath