In thermodynamics, branches of thermodynamics refers to the view of thermodynamics as a tree of knowledge with roots, sprouts, a trunk, and various branches, and spores and or seeds.

Overview
Thermodynamics has it roots in those as affinity-chemistry (1718), thermo-chemistry (1770s), thermo-electricity (1822), thus becoming a tree with foundations in the works of Sadi Carnot, William Thomson, Rudolf Clausius (trunk), and William Rankine, soon thereafter sprouting many branches, e.g. human thermodynamics (1952), and sub-branches of thermodynamics.

The following quote by Elias Gyftopoulos and Gian Beretta, gives an idea of the number of branches involved: [1]

“Physics is the science that attempts to describe all aspects of all phenomenon pertaining to the perceivable universe … it can be viewed as a large tree with many branches, such as mechanics, electromagnetism, gravitation, and chemistry, each specialized in the description of a particular class of phenomenon … thermodynamics [however] is not a branch … it pervades the entire tree.”

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Roots
Thermodynamics has its roots in Boerhaave's Law (1620), Guericke's vacuum pump (1645), the gas laws (1662-1809), dynamics (1686), Papin’s steam engine (1690), affinity-chemistry (1718), thermo-chemistry (1760s), caloric theory (1770s), kinetic theory of heat (1798), thermo-electricity (1822), thus becoming a sprouted tree with the seedling of Sadi Carnot’s 1824 treatise “Reflections on the Motive Power of Fire”, a seedling that was reformulated in graphical terms by Emile Clapeyron (1834) and later nurtured by William Thomson (1842), with a reformulation according to the mechanical equivalent of heat (1840s).

Newly added
● Mathematical thermodynamics
● Solution thermodynamics (link) (link)

Tree
The following set of tables, showing the thermodynamics tree (upside down), with German physicist Rudolf Clausius' 1865 textbook The Mechanical Theory of Heat forming the trunk** (with roots shown above), is a grouping and ordering of some of the various branches of thermodynamics:

Main Branches	System-specific Branches	Abstract Branches

Affinity-chemistry (1718)
Thermo-chemistry (1770s)
Thermo-electricity (1822)
"On the Motive Power of Fire" (1824)
Mechanical Theory of Heat (1865)
Classical thermodynamics (1850-99)
Statistical thermodynamics (1872-02)
Chemical thermodynamics (1876-23)
	Atmospheric thermodynamics (1888)
		Equilibrium thermodynamics
Engineering thermodynamics
	Chemical engineering thermodynamics (1925)	Information thermodynamics (1920s)
		Life thermodynamics (1920s)
		Quantum thermodynamics (1927)
		Relativistic thermodynamics (1930s)
		Nonequilibrium thermodynamics (1931)
		Computer science thermodynamics (1949)
	Ecological thermodynamics (1950s)
	Human thermodynamics (1952)
Biochemical thermodynamics (1957)

		Aerothermodynamics (1960s)
		Molecular thermodynamics (1960s)
		Surface thermodynamics (1960s)
	Geochemical thermodynamics (1964)	Earthquake thermodynamics (1964)
		Computational thermodynamics (1966)
		Network thermodynamics (1968)
	Cosmological thermodynamics (1970s)	Drug-receptor thermodynamics (1970s)
		Hierarchical thermodynamics (1978)


		Evolutionary thermodynamics
		Action thermodynamics (1980s)
		Supramolecular thermodynamics


		Nanothermodynamics (2001)
		Neurothermodynamics (2002)

The following are spin-off subjects related to thermodynamics or using thermodynamics as part of their composition:

● Stastistical mechanics (1901)
● Thermal physics (1910s)

References
1. Gyftopoulos, Elias P. and Berretta, Gian-Paolo. (2005). Thermodynamics: Foundations and Applications (pg. xv). New York: Dover.

Further reading
● Muschik, Wolfgang. (2008). "Survey of some branches of thermodynamics". J. Non-Equilib. Thermodyn. 33, 165-198.