Statistical distributions for Hamiltonian systems coupled to energy reservoirs and applications to molecular energy conversion

We study systems with Hamiltonian dynamics type coupled to reservoirsproviding free energy which may be converted into acceleration. Inthe first part we introduce general concepts, like canonical dissipative systemsand find exact solutions of associated Fokker–Planck equations thatdescribe time evolutions of systems at hand. Next we analyze dynamicsin ratchets with energy support which might be treated by perturbationtheory around canonical dissipative systems. Finally we discuss possibleapplications of these ratchet systems to model the mechanism of biologicalenergy conversion and molecular motors.