  In many different fields of science, it is useful to characterize physical
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 a theory of resources include: Which resources
can be converted into which other ones? What is the rate at which arbitrarily
many copies of one resource can be converted into arbitrarily many copies of
another? Can a catalyst help in making an impossible transformation possible?
How does one quantify the resource? Here, we propose a general mathematical
definition of what constitutes a resource theory. We prove some general
theorems about how resource theories can be constructed from theories of
processes wherein there is a special class of processes that are implementable
at no cost and which define the means by which the costly states and processes
can be interconverted one to another. We outline how various existing resource
theories fit into our framework. Our abstract characterization of resource
theories is a first step in a larger project of identifying universal features
and principles of resource theories. In this vein, we identify a few general
results concerning resource convertibility.
