Lewis inequality for a natural process
Summary the Lewis inequality for a natural process according to standard 1933 definition of English chemical thermodynamicist Edward Guggenheim. [1]
In inequalities, the Lewis inequality for a natural process, as contrasted with the Lewis inequality for an unnatural process, states that any natural change in a system, i.e. those which are actually observed in nature, must show a differential Gibbs free energy decrease if the process is to occur, which is quantified by the following inequality: [1]

dG lt 0

for a differential change in the system, or by the following expression:

DG lz c

for a change in the system on going from an initial state (in time) to a final state (in time). In hyperlinked form:

ΔG < 0

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]

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.

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