  Passivity is a fundamental concept in thermodynamics that demands a quantum
system's energy cannot be lowered by any reversible, unitary process acting on
the system. In the limit of many such systems, passivity leads in turn to the
concept of complete passivity, thermal states, and the emergence of a
thermodynamic temperature. In contrast, here we need only consider a single
system and show that every passive state except the thermal state is unstable
under a weaker form of reversibility. More precisely, we show that given a
single copy of any athermal quantum state we may extract a maximal amount of
energy from the state when we can use a machine that operates in a reversible
cycle and whose state is left unchanged. This means that for individual systems
the only form of passivity that is stable under general reversible processes is
complete passivity, and thus provides a single-shot and more physically
motivated identification of thermal states and the emergence of temperature.
The machine which extracts work from passive states exploits the fact that one
can find a subspace which acts as a virtual hot reservoir, and a subspace which
acts as a virtual cold reservoir. We show that an optimal amount of work can be
extracted, and that the machine operates at the Carnot efficiency between pairs
of virtual reservoirs.
