In the history of thermodynamics, entropy (misinterpretations) are a number of cases where scientists have gone on a false or misunderstood interpretation of German physicist Rudolf Clausius’ conception of entropy. There are many instances in which scientists who have never read any of Clausius’ papers or his textbook The Mechanical Theory of Heat, have spent years developing and promoting various interpretations of entropy, verbal and mathematical; often going on residual second or third, far-removed, interpretations, having little connection to the original meaning. The first to point out the difficulties involved in the understanding of entropy was American engineer Willard Gibbs, who in 1873 stated:


On this view, Gibbs devoted a section to discuss a few words on the terminology of the subject of "entropy", as the term and mathematical expression had been used differently by those as Clausius, Peter Tait, James Maxwell, and William Rankine. [1]

Maxwell
The classic example is Scottish physicist James Maxwell who had misinterpreted the meaning and mathematical sense of entropy, based on a reading of Peter Tait’s 1868 Sketch of Thermodynamics, that is until he read Willard Gibbs’ 1873 paper “Graphical Methods in the Thermodynamics of Fluids”, after which he was induced to make amendments and correct the text to the fourth edition of his Theory of Heat. In commentary in a letter to Tait on 01 December 1873, Maxwell states: [2][3]

“It is only lately, under the conduct of Professor Willard Gibbs that I have been led to recant an error which I had imbibed from your θΔcs namely that the entropy of Clausius is unavailable energy while that of T’ is available energy. The entropy of Clausius is neither the one nor the other it is only Rankine’s Thermodynamic Function.”

In a 27 March 1875 letter to James Thomson, Maxwell says: “I shall be very much obliged to you if you will let me know any suggestions, corrections, or amendments to my book on heat. A new edition is about to come out soon and several things must be modified, e.g. all about entropy and about the conditions of evaporation now solved by Gibbs.” [2] In the fourth edition of the text, to which he was referring, Maxwell made additions and revisions, correcting the erroneous discussion of “entropy” given in the earlier editions; see: Theory of Heat (London, 1875): 162-5 (“On Entropy”), 186-7, 187-93 (“Available energy”). He noted that in using the concept of “entropy” he was now following the meaning Clausius had attached to the term, and admitted that his earlier usage had introduced “great confusion into the language of thermodynamics”; Theory of Heat: 189n. [4]

Shannon
Another classic example is the story of how American chemical engineer John von Neumann, in the 1940s, suggestion to American engineer Claude Shannon to call phone line information signals, or loss thereof, “entropy” and thus gave birth to the grandly confused idea of "information entropy", often naively seen to have a thermodynamic basis.

Lambert
In decade surrounding 2002, with the publication of “Disorder: A Cracked Crutch for Supporting Entropy Discussions”, American chemist Frank Lambert is known to have made an uneducated push to get the word “disorder”, of the Boltzmann-Planck quantum mechanical origin, removed from America’s college chemistry textbooks and replaced with his simplified theory of “energy dispersion”, even though he has never, admittedly, read the works of Clausius, but rather derived his interpretation of entropy based on papers from William Thomson. [6]

His ubiquitous websites, such as SecondLaw.com, 2ndLaw.com, Shakespeare2ndLaw.com, EntropySimple.com, EntropySite.com, etc., have supposedly educated millions of students to the correct view of what entropy is. In addition, as of 2007, Lambert has aggressively petitioned a larger number of American chemistry textbook authors to replace the word disorder from their entropy chapters and to replace it with an energy dispersal view of entropy. Lambert claims to have convinced over a dozen different chemistry textbook authors to remove the word “disorder” from their chapters on entropy and thermodynamics, which as Google books shows (search: entropy, energy dispersal), is rather accurate estimate. All-in-all, this situation of reverse education seems to exemplify a case of the blind leading the blind.

Kennedy
Another example of entropy misinterpretation is Austrian environmental chemist Ivan Kennedy, who having never read the works of Clausius has developed a unit-less variation of entropy, on what seems to have no foundation, in a theory of what he calls action thermodynamics. [5] Kennedy, for instance, uses a large amount of standard thermodynaics terminology, e.g. free energy, internal energy, systems, etc., in discussion, but defines entropy as "a dimensionless capacity factor, the ratio of the cumulative heat needed to raise the temperature to T, divided by the absolute temperature, the latter being considered an energy intentsity factor." [7] On this logic, things become even more convoluted. The change in enthalpy ΔH, for instance, is defined by Kennedy as “changes in internal molecular entropy.” [8]

References
1. Gibbs, J. Willard. (1873). "A Method of Geometrical Representation of the Thermodynamic Properties of Substances by Means of Surfaces" (pgs. 51-52), Transactions of the Connecticut Academy, II. pp.382-404, Dec.
2. Maxwell, James, (Harman, Peter (editor)). (1990). The Scientific Letters and Papers of James Clerk Maxwell: 1874-1879 (Numbers 557 Letter to James Thomson, 27 March 1875, note (2) (pg. 205), 587 Draft of ‘On the Equilibrium of Heterogeneous Substances, circa February 1876, note (7) (pg. 283), and 623 Letter to Peter Guthrie Tait, note (4) (pg. 397)). Cambridge University Press.
3. See: J. Willard Gibbs, “Graphical Methods in the Thermodynamics of Fluids”, (Gibbs quote: “the term entropy, it will be observed, is here used in accordance with the original suggestion of Clausius, and not in the sense in which it has been employed by Professor Tait and others after his suggestion. The same quantity has been called by Professor Rankine the Thermo-dynamic function.”) Transactions of the Connecticut Academy of Arts and Sciences, 2 (1873): 309-42, esp. 310n.
4. (a) On his clarification of “entropy” see his letter to Tait of 01 December 1873 (Volume II: 945-6, and see Number 529 note (6)).
(b) On these revisions to the Theory of Heat see Edward Daub, “Entropy and Dissipation”, Historical Studies in the Physical Sciences, 2 (197): 321-54, esp. 330-3.
5. Kennedy, Ivan R. (2001). Action in Ecosystems: Biothermodynamics for Sustainability (ch. 4: Action Thermodynamics, pgs. 65-98). Research Studies Press.
6. (a) Email commentary from Lambert to Libb Thims in connection to Wikipedia Talk Page discussions, c. 2006-2007.
(b) Entropy (energy dispersal) - Wikipedia.
7. Rose, M.T., Crossan, A.N. and Kennedy, I.R. (2008). “ Sustaining Action and Optimising Entropy: Coupling Efficiency for Energy and the Sustainability of Global Ecosystems”. Bulletin of Science, Technology and Society, 28, 260-272.
8. Email commentary from Kennedy to Libb Thims on 02 January 2009.
9. Lambert, Frank L. (2002). “Disorder: A Cracked Crutch for Supporting Entropy Discussions”, Journal of Chemical Education, 79: 187-92.