Controlled transport in complex fluids is a challenge in biotechnology and microfluidics.A temperature gradient induces a movement of solutes: the Soret effect or thermophoresis.The diffusion coefficient which appears in Onsagers phenomenological relation for the transport speed depends on the solute considered.This allows for example to separate species in a micro channel.For thermodiffusion of polymers,it was shown that the transport coefficient has two contributions of different origins: first,dispersion forces between solvent and solute pushes it to cold areas,and secondly,a gradient of chemical potential of the solvent acts as a generalized force on the solute and promotes it to hot areas.The competition of these opposite effects explains the variation with the molecular weight of polymer diffusion coefficient,which can change sign.As a toy model for this problem,we looked at the example of the Rayleigh piston: in a cylinder,an adiabatic piston fluctuates because of collisions with the two gases which it separates.Even if the pressures in the two semi-infinite reservoirs are equal,the system is out of equilibrium when the temperatures are different and the piston acquires a nonzero average velocity,proportional to temperature gradient.There is a heat transfer between the two gases: the piston acts as a rectifier of fluctuations of Brownian motion.This heat flow is causing a flow of entropy that we have calculated,together with the work of the generalized force.