An example of Gibbs free energy G as a function of the extent x of a process or reaction with plot (a) showing a generic reaction as it is assumed to occur and (b) showing a hypothetical reaction that is not possible or assumed not to ever occur. [4]
In chemistry, extent of reaction, or "reaction extent", symbol ξ, or Greek letter xi, or sometimes x, is an extensive quantity describing the progress of a chemical reaction equal to the number of chemical transformations, as indicated by the reaction equation on a molecular scale. [1]

Mathematically, extent of reaction or ‘extent of process’ refers to the partial differential of a thermodynamic potential, predominantly Gibbs free energy change G, with respect to the partial differential of an extent variable x, such as concentration or time, with specified variables assumed to be held constant, generally temperature T and pressure P, meaning loosely a non-heated open atmospheric reaction:

$\Bigg ( \frac{\partial G}{\partial x} \Bigg )_{T,P} \,$

 With marriage viewed as a human chemical reaction, the factoid of 43% of marriages ending at 15 years, is a measure of the extent of reaction.
When this expression is equal to zero the reaction or process is said to be at the equilibrium position at the bottom of potential energy well curve.

The extent of reaction is essentially the amount of chemical transformations. The extent of reaction also goes by various other names such as reaction coordinate ε or degree of advancement, degree of reaction, and progress variable, all of which characterize the extent or degree to which a reaction has taken place. [2]

History
The variable
extent, symbol ξ, was introduced by Belgian mathematical physicist Théophile de Donder in 1920. [3]