# ΔG > 0

In equations, the following formula:

$\Delta G > 0 \,$

is called the Lewis inequality for an unnatural process and states that the difference of the Gibbs free energy, symbol "G", of an isothermic-isobaric system in its final state Gf less the Gibbs free energy of the system in its initial state Gi, is greater than zero, where ΔG is equal to:

$\Delta G = G_f - G_i \,$

the symbol "Δ", the Greek capital letter Delta, being the thermodynamics symbol for a large change (in contrast with a small differential change, symbol "d" or "δ" (delta), for an exact differential change, or $\bar{d} \,$(d-hat) or đ (d-crossbar), for an inexact differential change), the symbol ">" being the greater than inequality mathematical symbol. [1] A synonymous name of this equation is the: Gibbs free energy change for a non-spontaneous process.

History
This equation was first stated by American physical chemist Gilbert Lewis in 1923, based on the 1876 work of American engineer Willard Gibbs, which in turn is based on the 1856 Clausius inequality, developed by German physicist Rudolf Clausius, which in turn is based on the the principle of Carnot efficiency, developed in 1824 by French physicist Sadi Carnot.

References
1. Guggenheim, Edward, A. (1933). Modern Thermodynamics by the Methods of Willard Gibbs (pg. 17). London: Methuen & Co.
2. Lewis, Gilbert N. and Randall, Merle. (1923). Thermodynamics and the Free Energy of Chemical Substances (pgs. 160-61). McGraw-Hill Book Co., Inc.