A diagram of the various "branches" and "roots" of the tree of thermodynamics, having the mechanical theory of heat as its trunk.

In theories, the mechanical theory of heat or Mechanische Wärmetheorie (German) is a unification of Boerhaave’s law, the theory of heat, mechanical theory, specifically the mechanical logic of the steam engine operation, the mechanical equivalent of heat, utilizing parts of the kinetic theory, and the ideal gas laws, among other topics (such as electrochemistry), as presented in German physicist Rudolf Clausius’ 1865 textbook The Mechanical Theory of Heat. [1]

References
1. (a) Clausius, R. (1865). The Mechanical Theory of Heat – with its Applications to the Steam Engine and to Physical Properties of Bodies. (Google Books). London: John van Voorst, 1 Paternoster Row. MDCCCLXVII.
(b) Clausius, Rudolf. (1879). The Mechanical Theory of Heat, (2nd ed). London: Macmillan & Co.