Entropy is the uncertainty or disorder in a system. In a technical sense, it is the gradual breakdown of energy and matter in the universe; in casual usage, it refers to degradation or disorder in any situation, or to chaos, disorganization, or randomness in general. The stem -tropy, from the Greek word trope, means “change” or “turn.”
It’s easily confused with a similar-sounding but unrelated word: atrophy, which refers to physical or psychological decline: Atrophy, which serves as a verb as well, stems from the Greek word trephein, which means “to nourish”; the prefix a- indicates antonymic form, as in apolitical or atheism.
Atrophy can also mean poor development or loss of a part of an animal or plant, and in that sense it’s related to dystrophy, which in general refers to a condition resulting from poor nutrition, though it’s more familiar as part of the phrase “muscular dystrophy”; that, by contrast, identifies a hereditary disease that results in wasting away of muscle tissue.
Trophy, however, meaning “a prize” or “a memorial,” is — despite the ph spelling — from trope, not trephein. (It evolved from a second sense of trope as “a rout, a victory.”) It’s related, therefore, to the English word trope, which refers to a figure of speech or a cliché (a “turn” of phrase); the primary sense of that word is “a device or theme,” as in a common and perhaps trite plot element in a war movie or a tearjerker.
Trop- features at the head of other words, too: tropic, referring to the two parallel lines of latitude that cross over the tropics, and tropism, which means “a tendency, inclination, or propensity.” The syllable also appears in numerous medical and scientific terms, such as autotropism and somatotropin.