  Based only on classical Hamiltonian dynamics, we prove the maximum work
principle in a system where macroscopic dynamical degrees of freedom are
intrinsically coupled to microscopic degrees of freedom. Unlike recent
identities between irreversible work and free energy, such as in the Jarzynski
relation, the macroscopic dynamics is not governed by an external action but
undergoes the back reaction of the microscopic degrees of freedom. Our theorems
cover such physical situations as impact between macroscopic bodies,
thermodynamic machines, and molecular motors.
