A mathematical theory of resources

Many fields of science investigate states and processes as resources. Chemistry, thermodynamics, Shannon's theory of communication channels, and the theory of quantum entanglement are prominent examples. Questions addressed by these theories include: Which resources can be converted into which others? At what rate can many copies of one resource be converted into many copies of another? Can a catalyst enable a conversion? How to quantify a resource? We propose a general mathematical definition of resource theory. We prove general theorems about how resource theories can be constructed from theories of processes with a subclass of processes that are freely implementable. These define the means by which costly states and processes can be interconverted. We outline how various existing resource theories fit into our framework, which is a first step in a project of identifying universal features and principles of resource theories. We develop a few general results concerning resource convertibility.