Resource theories with completely passive states and passive states as free states

Work extractable from quantum system can be viewed as a resource to perform some tasks. Here, we try to related the work extractable to some resource theory. To do this, we consider completely passive states and passive states as free states and we formulate resource theories where the maximum work extractable is a monotone, by identifying the free operations. In particular, we study how the free operations act on the free states, showing how a sort of temperature plays a pivotal role in these resource theories.