In thermodynamics, state function is an exact or complete differential that defines the physical condition (configuration) or state of a system in a manner that is independent in how the system arrived at that state; quantities that depend on the ‘state’ of the system only and not, e.g., on its history. [1]

History
The concept of "state function", according to Leslie Woodcock, supposedly, was first introduced, in proto-conceptual outline, by Joseph Black (1728-1799), in his caloric theory of heat; the gist of his assertion stated as follows: [6]

“Of great fundamental relevance, however, and largely overlooked by historians of science, is the fact that Black had for the first time, it appears, introduced the concept of a state function. The properties of a material (in this case the caloric content) depend only upon its equilibrium state and not on its processing history. The total energy of a material is the thermodynamic state function called the “internal energy.” Only differences in energy between two states can be defined and measured. If those two states are at the same pressure, the energy difference is called the ‘enthalpy’. This thermodynamic state function can be identified with Black’s ‘caloric’.”

In 1869, French engineer Francois Massieu, in his “On the Various Functions Characteristic of Fluids”, introduced the concept of the existence of characteristic functions; which in 1876 was adopted by Willard Gibbs, into what are now referred to as state functions, or functions characteristic of the state of a given body. [7]

Social systems | Applicability debate
See main: Social equation of state
There seems to exist a variable opinion as to how, when, and where state functions, such as internal energy U, free energy F or G, or entropy S, etc., apply and if, specifically, they apply to a collection or system of people, such as a town. The 2006 Rossini-Leonard-Wojcik debate is a prime example, wherein it became sort of a debate of whether one can apply state functions to humanity, prompting response articles such as "State Functions v. State Governments". Various contrasting views are discussed below:

In 1809, German polymath Johann Goethe put forth a theory that chemical affinity A applies to the regulation of human activity, viewed as chemical reactions. [2] After 1882, wherein after German physicist Hermann Helmholtz showed that chemical affinity is measure by the change in free energy, Goethe’s theory amounts to the argument that changes in the state function Gibbs free energy (A = - ΔG ) is what regulates or predetermines human movements.

In 1914, English-born American engineer William Fairburn suggested that one could measure both an energy and and entropy of people viewed as 'human chemical elements'. [5]

One dominate point of view comes from the Prigogine school, a group which argues that only certain state functions modified to fit the non-equilibrium regime apply to biological systems or human systems, whereas others do not apply. The central message comes from, in his 1977 Nobel Lecture, Belgian chemist Ilya Prigogine commented that: [3]

“Thermodynamic equilibrium may be characterized by the minimum of the Helmholtz free energy, defined usually by F = E – TS. Are most types of organizations around us of this nature? It is enough to ask such a question to see that the answer is negative. Obviously in a town, in a living system, we have quite different type of functional order. To obtain a thermodynamic theory for this type of structure we have to show that non-equilibrium may be a source of order. Irreversible processes may lead to a new type of dynamic states of matter which I have called dissipative structures.”

Likewise, in 2005, Danish ecological engineer and Prigogine advocate Sven Jorgenson commented that: [4]

Evolution and biological growth [occur] away from thermodynamic equilibrium [and] entropy can be used to describe systems far from thermodynamic equilibrium, provided that it is applied as a non-state function. Free energy and entropy are not state functions when applied on living organisms or ecosystems. At death, the organisms lose a major part of their free energy (eco-exergy) and produce an enormous amount of entropy (Schrodinger would say that they lose negentropy), because the free energy of the information embodied in the genes are no longer applicable.”

The prevailing view of this school is that free energy and entropy are not state functions of a form that can be used to quantify life (reaction existence).

References
1. (a) Perrot, Pierre. (1998). A to Z of Thermodynamics (pg. 298). Oxford: Oxford University Press.
(b) Waser, Jurg. (1966). Basic Chemical Thermodynamics (pg. 11). W.A. Benjamin, Inc.
2. (a) Goethe, Johann. (1809). Elective Affinities. Tubingen.
(b) Thims, Libb. (2007). Human Chemistry (Volume Two) (ch. 10: "Goethe's Affinities", pgs. 371-422). Morrisville, NC: LuLu.
3. Prigogine, Ilya. (1977). “Time, Structure and Fluctuations”. Nobel Lecture. Dec. 08.
4. Jorgenson, Sven. (2005). “preface”; in Steps Towards an Evolutionary Physics (pgs. ix-xi) by Enzo Tiezzi . WIT Press, 2006.
5. Fairburn, William Armstrong. (1914). Human Chemistry. The Nation Valley Press, Inc.
6. (a) Black, Joseph. (1809). Lectures on the Elements of Chemistry (editor: J. Robinson). University of Edinburgh.
(b) Woodcock, Leslie V. (2005). “Phlogiston Theory and Chemical Revolutions” (Ѻ), Bulletin of the History of Chemistry, 30(2):63-69.
7. (a) Massieu, Francois. (1869). “Sur les Functions Caracteristiques des Divers Fluides et Sur la Theorie des Vapeurs (On the Various Functions Characteristic of Fluids and on the Theory of Vapors)”, Comptes Rendus, 69: 858-62, 1057-61.
(b) Massieu, Francois. (1876). Thermodynamique: Mêmoire sur les fonctions catactéristiques des divers fluides et sur la théorie des vapeurs. 92-pgs. Académie des Sciences de L'Institut National de France.
(c) Gibbs, Willard. (1876). "On the Equilibrium of Heterogeneous Substances" (Massieu, pgs. 86, 358),Transactions of the Connecticut Academy,III. pp. 108-248, Oct., 1875-May, 1876, and pp. 343-524, may, 1877-July, 1878.