  Thermodynamics, which describes vast systems, has been reconciled with small
scales, relevant to single-molecule experiments, in resource theories. Resource
theories have been used to model exchanges of energy and information. Recently,
particle exchanges were modeled; and an umbrella family of thermodynamic
resource theories was proposed to model diverse baths, interactions, and free
energies. This paper motivates and details the family's structure and
prospective applications. How to model electrochemical, gravitational,
magnetic, and other thermodynamic systems is explained. Szilard's engine and
Landauer's Principle are generalized, as resourcefulness is shown to be
convertible not only between information and gravitational energy, but also
among diverse degrees of freedom. Extensive variables are associated with
quantum operators that might fail to commute, introducing extra nonclassicality
into thermodynamic resource theories. An early version of this paper partially
motivated the later development of noncommutative thermalization. This
generalization expands the theories' potential for modeling realistic systems
with which small-scale statistical mechanics might be tested experimentally.
