In economic thermodynamics, material entropy is an approximate or rather contrived term, a spinoff of the term "bound energy", used to define the amount of entropy or order associated with a structure, the structure tending to be some type of natural resource, as in coal.

Etymology
In 1966, Kenneth Boulding, an English-born American economist, in a paper titled “The Economics of the Coming Spaceship Earth”, supposedly, coined the term as follows: [1]

“In the case of material systems, we can distinguish between entropic processes, which take concentrated materials and diffuse them through the oceans or over the earth's surface or into the atmosphere, and anti-entropic processes, which take diffuse materials and concentrate them. Material entropy can be taken as a measure of the uniformity of the distribution of elements and, more uncertainly, compounds and other structures on the earth's surface. There is, fortunately, no law of increasing material entropy, as there is in the corresponding case of energy, as it is quite possible to concentrate diffused materials if energy inputs are allowed. Thus the processes for fixation of nitrogen from the air, processes for the extraction of magnesium or other elements from the sea, and processes for the desalinization of sea water are anti-entropic ill the material sense, though the reduction of material entropy has to be paid for by inputs of energy and also inputs of information, or at least a stock of information in the system. In regard to matter, therefore, a closed system is conceivable, that is, a system in which there is neither increase nor decrease in material entropy. In such a system all outputs from consumption would constantly be recycled to become inputs for production, as for instance, nitrogen in the nitrogen cycle of the natural ecosystem.”
— Kenneth Boulding (1966), “The Economics of the Coming Spaceship Earth” (pg. 3) [5]

In 1971, Nicholas Roegen, in his The Entropy Law and the Economic Process, outlined a type of material entropy theory by stating that “entropy is an index of the relative amount of bound energy in an isolated structure or, more precisely, of how evenly the energy is distributed in such a structure”. In other words, he states, “high entropy means a structure in which most or all energy is bound, and low entropy, a structure in which the opposite is true”.

In 1980, Jeremy Rifkin, stimulated by Boulding and Roegen, in Entropy: A New World View, a supposed fourth law of thermodynamics: “in a closed system, the material entropy must ultimately reach a maximum”, which he translated into the postulate that humans are squandering the world's natural resources.


A basic thermodynamic database table showing, in the fifth column, entropies S of different types of chemicals (matter).

A basic thermodynamic database table showing, in the fifth column, entropies S of different types of chemicals (matter).

Difficulties on term
Material entropy, as generally found, is a spinoff term having little theoretical substance to it. Some will state, for instance, that “there is, fortunately, no law of increasing material entropy, as there is in the corresponding case of energy, as it is quite possible to concentrate diffused materials if energy inputs are allowed.” [2]

The general difficulty of using the concept of material entropy, beyond that involved in the formation of small molecules or small chemical systems, is that, in the words of Rudolf Clausius: [3]

“It is not possible to determine the whole energy of a body, but only the increase which the energy has received, whilst the body was passing into its present condition; and the same is also true of entropy”.

Shown adjacent, for instance, are various measures of entropies S° for different chemical species. In other words, the entropies of bodies, depend upon various factors involved related to the heats and energies released or absorbed during their formation, and are based on reference points. It is not simply a matter of assigning low entropy values to ordered structures, e.g. coal, and high entropy values to disordered structures, e.g. burned coal and waste gas.

Objections
The use of material entropy, as seeded by Georgescu-Roegen and promulgated by Rifkin, is generally seen as point of non-logic. Israeli physical chemist Brian Silver, in commentary on what he calls “Georgescu-Roegen’s brainchild”, for instance, states that “the term material entropy is meaningless; it has not the slightest connection with entropy. [4] Likewise, American chemist Glen Gordon states that “in taking up entropy, Rifkin is like a child with a new toy—he has great fun applying the concepts to all aspects of our high-technology society.” [5]

In 2004, American-born Australian economist Elias Khalil published his “The Three Laws of Thermodynamics and the Theory of Production”, which he had reviewed by: Jeffrey Wicken, Reiner Kummel, Kozo Mayumi, among others, wherein he argues the following position: [1]

“This paper concurs with experts on thermodynamics that Georgescu-Roegen has committed a major error. Georgescu-Roegen’s notion of ‘material entropy’, which he christened as the ‘fourth law of thermodynamics’, is unfounded.”

Khalil concludes that Georgescu-Roegen's purported law, as the application of the second law to the realm of matter, is a grave conceptual blunder. [6]

References
1. Boulding, Kenneth E. (1966). "The Economics of the Coming Spaceship Earth", presented at the Sixth Resources for the Future Forum on Environmental Quality in a Growing Economy in Washington, D.C. (Mar 8); in H. Jarret, ed., Environmental Quality in a Growing Economy. Johns Hopkins University Press.
2. Lippit, Victor D. (1995). Radical Political Economy: Explorations in Alternative Economic Analysis, (pg. 360). M.E. Sharpe.
3. Clausius, Rudolf. (1879). The Mechanical Theory of Heat, (chapter IX: "Determination of Energy and Entropy", pg. 196). London: Macmillan & Co. (second edition).
4. Silver, Brian L. (1998). The Ascent of Science, (pg. 231). Oxford University Press.
5. Gordon, Glen E. (1981). “Thermodynamics and Society” (review of Rifkin’s Entropy: A New World Order), Science, Vol. 211, March. 1340-41.
6. (a) Khalil, Elias. (2004). “The Three Laws of Thermodynamics and the Theory of Production.” (abs) Journal of Economic Issues, March, 38:1, pp. 201-226.
(b) Staff Writer. (2004). “The Three Laws of Thermodynamics and the Theory of Production”, RedOrbit News, March 13.