  Engines are open systems that can generate work cyclically, at the expense of
an external disequilibrium. They are ubiquitous in nature and technology, but
the course of mathematical physics over the last 300 years has tended to make
their dynamics in time a theoretical blind spot. This has hampered the
usefulness of statistical mechanics applied to active systems, including living
matter. We argue that recent advances in the theory of open quantum systems,
coupled with renewed interest in understanding how active forces result from
positive feedback between different macroscopic degrees of freedom in the
presence of dissipation, point to a more realistic description of autonomous
engines. We propose a general conceptualization of an engine that helps clarify
the distinction between its heat and work outputs. Based on this, we show how
the external loading force and the thermal noise may be incorporated into the
relevant equations of motion. This modifies the usual Fokker-Planck and
Langevin equations, offering a thermodynamically complete formulation of the
irreversible dynamics of simple oscillating and rotating engines.
