Work extraction and thermodynamics for individual quantum systems

Understand

Thermodynamics is traditionally concerned with systems comprised of a large number of particles.

• Here we present a framework for extending thermodynamics to individual quantum systems, including explicitly a thermal bath and work-storage device (essentially a `weight' that can be raised or lowered).
• We prove that the second law of thermodynamics holds in our framework, and give a simple protocol to extract the optimal amount of work from the system, equal to its change in free energy.
• Our results apply to any quantum system in an arbitrary initial state, in particular including non-equilibrium situations.