#(Insert I-Am-Not-A-Physicist Standard Disclaimer Here)
Either the description given above is too vague, or this device already exists (in my secret underground laboratory, muhahaha!). Unsurprisingly for some, cells use Brownian Motion to their advantage. A specific example might be the cytoskeleton - a network of protein filaments that criss-crosses the cytoplasm. Actin (a particular type of filament protein) can add monomers at one end or lose them from the other. As a consequence of this behaviour, short actin filaments can push membranes outward - the filament bends enough to allow a new monomer to slip onto the end. The filament straightens, pressing against the bilayer and so deforming the surface.
It is this kind of mechanism that allows cells to create pseudopods to engulf food, push stalks up into the air and even make connections in the brain (not synaptic connections, other kinds). Also, the motors that run up or down (not always both) the cytoskeletal filaments are such Brownian Machines, somehow they possess a direction that works against the background bombardment of water and free floating proteins. Admittedly, most of these devices use some sort of 'chemical energy' to change state - actin monomers break down ATP while binding to f-Actin (the polymer) while tubulin monomers use GTP.