"a form in which an element having the property of allotropy may exist," 1847, a back-formation from allotropy "variation of physical properties without change of substance," from Greek allotropos "in another manner;" see allo- "different" + -trope "way, manner." Diamond is an allotrope of carbon. Related: Allotropic.
1540s, "body of soldiers," 1540s, from French troupe, from Old French trope "band of people, company, troop, crowd" (13c.), a word of uncertain origin, perhaps from Frankish *throp "assembly, gathering of people" or another Germanic source, perhaps related to Old English ðorp, Old Norse thorp "village" (see thorp). OED derives the French word from Latin troppus "flock," which is of unknown origin but also might be from the proposed Germanic source. Of groups of animals from 1580s. Specifically as "a subdivision of a cavalry force" from 1580s; of Boy Scouts from 1908. Troops "armed forces" is from 1590s.
in rhetoric, a trope or figure of speech in which the name of one thing is substituted for that of another that is suggested by or closely associated with it (such as the bottle for "alcoholic drink," the Kremlin for "the Russian government"); 1560s, from French métonymie (16c.) and directly from Late Latin metonymia, from Greek metōnymia, literally "change of name," related to metonomazein "to call by a new name; to take a new name," from meta "change" (see meta-) + onyma, dialectal form of onoma "name" (from PIE root *no-men- "name"). It often serves to call up associations not suggested by the literal name. Related: Metonymic; metonymical; metonymically.
The notion is of the point at which the sun "turns back" after reaching its northernmost or southernmost point in the sky. Extended 1520s to the corresponding latitudes on the earth's surface (23 degrees 28 minutes north and south); meaning "region between the tropics of Cancer and Capricorn" is from 1837.
1868, from German Entropie "measure of the disorder of a system," coined 1865 (on analogy of Energie) by German physicist Rudolph Clausius (1822-1888), in his work on the laws of thermodynamics, from Greek entropia "a turning toward," from en "in" (see en- (2)) + trope "a turning, a transformation" (from PIE root *trep- "to turn"). The notion is supposed to be "transformation contents." Related: Entropic.
It was not until 1865 that Clausius invented the word entropy as a suitable name for what he had been calling "the transformational content of the body." The new word made it possible to state the second law in the brief but portentous form: "The entropy of the universe tends toward a maximum," but Clausius did not view entropy as the basic concept for understanding that law. He preferred to express the physical meaning of the second law in terms of the concept of disgregation, another word that he coined, a concept that never became part of the accepted structure of thermodynamics. [Martin J. Klein, "The Scientific Style of Josiah Willard Gibbs," in "A Century of Mathematics in America," 1989]