  Passive states are defined as those states that do not allow for work
extraction in a cyclic (unitary) process. Within the set of passive states,
thermal states are the most stable ones: they maximize the entropy for a given
energy, and similarly they minimize the energy for a given entropy. Here we
find the passive states lying in the other extreme, i.e., those that maximize
the energy for a given entropy, which we show also minimize the entropy when
the energy is fixed. These extremal properties make these states useful to
obtain fundamental bounds for the thermodynamics of finite-dimensional quantum
systems, which we show in several scenarios.
