A Resource Theory for Work and Heat

Several recent results in the field of quantum thermodynamics have been obtained using the tools of quantum information theory and resource theories. So far, the resource theories utilised to describe quantum thermodynamics have assumed the existence of an infinite thermal reservoir, by declaring that thermal states at some background temperature come for free. Here, we propose a resource theory of quantum thermodynamics without a background temperature, so that no states at all come for free. In this resource theory, we show that states are classified up to many-copy equivalence by their entropy and average energy, which implies that thermodynamics takes place in a two-dimensional convex set that we call the energy-entropy diagram. The answers to many resource-theoretic questions about thermodynamics can be read off from this diagram, such as the efficiency of a heat engine consisting of finite reservoirs or the rate of conversion between two states. This allows us to consider a resource theory which puts work and heat on an equal footing, and serves as a model for more general resource theories.