|Summary the Lewis inequality for a natural process according to standard 1933 definition of English chemical thermodynamicist Edward Guggenheim. |
for a differential change in the system, or by the following expression:
for a change in the system on going from an initial state (in time) to a final state (in time). In hyperlinked form:
The Lewis inequality for a "natural process", of the two types of Lewis inequalities, is the inequality for a spontaneous process or reaction. The ‘type’ of systems here being closed isothermal-isobaric systems not harnessed in some way for the production of useful work, which include the common cases of reactions which ‘run freely’, like the combustion of a fuel, the action of an acid upon metal, or a reaction between two people on the surface of the earth. 
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.