In theoretical thermodynamics, respected authors vary in their approaches to the definition of quantity of heat transferred.
One is from a primarily empirical viewpoint (which will here be referred to as the thermodynamic stream), to define heat transfer as occurring only by specified macroscopic mechanisms; loosely speaking, this approach is historically older.
The other (which will here be referred to as the mechanical stream) is from a primarily theoretical viewpoint, to define it as a residual quantity after transfers of energy as macroscopic work, between two bodies or closed systems, have been determined for a process, so as to conform with the principle of conservation of energy or the first law of thermodynamics for closed systems; this approach grew in the twentieth century, though was partly manifest in the nineteenth.
These two concepts are coordinately coherent in the sense that they arise jointly in the description of experiments of transfer of energy as heat.
Axiomatic presentations of this stream of thinking vary slightly, but they intend to avoid the notions of heat and of temperature in their axioms.
The authors Buchdahl, Callen, and Haase make no mention of the passage of radiation, thermal or coherent, across their adiabatic walls.
Carathéodory explicitly discusses problems with respect to thermal radiation, which is incoherent, and he was probably unaware of the practical possibility of laser light, which is coherent.
Another text considers asbestos and fiberglass as good examples of materials that constitute a practicable adiabatic wall.
[14] The mechanical stream of thinking thus regards the adiabatic enclosure's property of not allowing the transfer of heat across itself as a deduction from the Carathéodory axioms of thermodynamics.