In thermodynamics, the Gibbs equation or Gibbs free energy equation (also Gibbs function) refers to the basic equation for the Gibbs free energy change Δ for isothermal-isobaric chemical reactions occurring in a closed system:
ΔG = ΔH – TΔS
where ΔG is the change in the Gibbs free energy, ΔH the change in the enthalpy, T the temperature, and ΔS the change in the entropy of the system on going from its initial state to its final state, respectively. This equation, which is the best-known chemical thermodynamics equation to chemistry students, is the also called the combined law of thermodynamics, is a derivative of the more advanced Gibbs fundamental equation, and can be thought of as the cliff notes version of American engineer Willard Gibbs’ 1876, 700-equation, treatise On the Equilibrium of Heterogeneous Substances.
The change in Gibbs free energy embodies the directionality of natural processes in human social interactions as quantified by the spontaneity criterion.  As explained in American physical chemist Thomas Wallace’s 2009 appendix section ‘The Fundamentals of Thermodynamics Applied to Socioeconomics’: 
“The thermodynamic parameter free energy, mathematically defined by ΔG = ΔH – TΔS, represents the fundamental driving force in nature and determines whether physical and chemical processes conducted by nature and society will take place.”
Wallace explains further that free energy is ‘nature’s intrinsic dynamic force, representing the probability parameter entropy S and the energy content parameter enthalpy.’ In more correct detail, Wallace, here, to note, is using Boltzmann-Planck type entropy descriptions, which are specifically culled from gas theory, wherein the particles are said to have a non-correlation of velocities. Humans, however, have correlated velocities; subsequently it is necessary to return to the original work of Clausius and his universal description of entropy change as the ‘equivalence value of all uncompensated transformations’, to human social transformation. Beyond this, enthalpy is not simply an ‘energy content parameter’, but one must use the full expression for enthalpy:
ΔH = ΔU + PΔV
to study human social systems in terms of both internal energy changes ΔU and the work-energy PΔV associated with volume changes ΔV in systems, such as exemplified by the volume change in territory in the course of the rise and fall of Rome during a 1,000-years of human expansion and contraction reactions.
● Gibbs-Helmholtz equation
● Gibbs-Duhem equation
● Gibbs entropy
● Gibbs energy flow
1. Mascetta, Joseph A. (2008). Barron’s SAT Subject Test Guide (Gibbs equation, pg. 242). Barron’s Educational Series.
2. (a) Thims, Libb. (2007). Human Chemistry (Volume One). Morrisville, NC: LuLu.
(b) Thims, Libb. (2007). Human Chemistry (Volume Two). Morrisville, NC: LuLu.
3. 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.