ΔG = ΔH – TΔS

In equations, the formula:

 \Delta G = \Delta H - T \Delta S  \,

is called the equation for "Gibbs free energy change" for a closed isothermic-isobaric reaction or process and states that the change, symbol "Δ", in Gibbs free energy, symbol "ΔG", over the extent of the reaction or process, on transforming from an initial state to a final state, is equal to the change in enthalpy, symbol "ΔH", less the product of the absolute temperature, symbol "T", of the system, and the entropy change, symbol "ΔS", of the process.

History
The above equation, albeit not exactly in the shown notation, was first derived in the 1873 work of American engineer Willard Gibbs. The first to start using the delta symbol notation, it seems, was American physical chemist Gilbert Lewis in 1923. In 1933, the function began to be specifically called "Gibbs free energy" but English physicist Edward Guggenheim.

Humans
The above function is the main governing equation of human existence, as defined by the Lewis inequality for natural processes (ΔG < 0). This view is expressed well by American physical chemist Thomas Wallace who in his 2009 appendix section "The Fundamentals of Thermodynamics Applied to Socioeconomics", states that the following about this equation:

“The spontaneity of a thermodynamic process is measured by its free energy change ΔG, which at constant temperature is mathematically represented by the function ΔG = ΔH – TΔS, whereby the parameters enthalpy H and entropy S represent the variables of heat content and probability, respectively, for the physical, chemical, and biological processes of nature and society, and where free energy G represents the fundamental driving force in nature and determines whether physical and chemical processes conducted by nature and society will take place.”

This quote is fairly representative of the view that has been emerging in the last decade or so.

References
1. Wallace, Thomas P. (2009). Wealth, Energy, and Human Values: the Dynamics of Decaying Civilizations from Ancient Greece to America (Appendix A: The Fundamentals of Thermodynamics Applied to Society, pgs. 469-89.). AuthorHouse.

External links
ΔG = ΔH – TΔS (Frank Lambert) – 2ndLaw.oxy.edu.
ΔG = ΔH – TΔS (Mr. Kent) – KentChemistry.com.

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