|The first extropy advertisement, used by Tom Bell and Max More in the Fall of 1988 to promote the first few issues of their journal. |
In 1967, or before Harry Overstreet, American naturalist humanist philosopher, introduced the term "extropy" as a counter-entropy quantity (see: entropy antonyms), which he defined as involving truth and beauty and goodness, would be expected to lead inevitably to god. 
One of the first mentions of the term extropy as a book title is the 1984 book Mythematics and Extropy, a work that seems to be associated with Polish poet Boleslaw Lesmian, who is noted for a number of neologisms.
Independently, it seems the term was coined, originating via analogy, by American lawyer-philosopher Tom Bell in 1988.  Max More, Bell's accociate, defines extropy as a "metaphor, loosely related to the idea of negentropy, that refers to basic attitudes and values shared by those who want to overcome human limits".  In 2010, when queried as to “the history behind adopting the term extropy, particularly in relation to either entropy or thermodynamics, as a type of philosophy?”, Tom Bell suggested the web archive Extropian FAQ page gave the best overview.
People considered to be adherents of the principles of extropy is called an "extropian" and the ideology or philosophy study of the subject is called "extropianism"
In August, of 1988, Bell together with English-American philosopher Max More started the printed journal Extropy, in which the term “extropy” was coined to define “the opposite of entropy or of thermodynamic decay”.  In the years to follow the term, both with and without thermodynamic qualifiers, slowly trickled into public use.
In 1999, American physican Karlis Ullis, within his theory of exercise physiology human thermodynamics, defined extropy as a state of antientropy, which leads to the building of organized biological structures, the ultimate blueprint that calls for sexual maturation and reproduction. 
In recent years, the term has come be associated with a creative force or élan vital, which is regarded by the new age and techno-utopian communities as generating novelty, breeding complexity, producing insights, and countering the forces of entropy. In this ideology, extropy is associated with the set of natural health products or ways of life, which mediate a type of force of extropy, that promote holistic well-being as they act to counter the entropic threat or degeneration.  These types of analogy uses, however, seem to have no rigorous connection to fundamental thermodynamics.
A recent popular search term is novelty vs extropy, which seems to be a revival of something called “novelty theory”, supposedly, developed by American new age philosopher Terence McKenna, which proposes that the universe is an engine designed for the production and conservation of novelty. Novelty, in this context, can be thought of as newness, or extropy (supposedly borrowed from Max More’s meaning of the opposite of entropy). Some kind of laymanized view holds that, in a nutshell, novelty theory involves ontology, extropy, and eschatology. According to McKenna, when novelty is graphed over time, a fractal waveform known as "timewave zero" or simply the "timewave" results. The graph shows at what time periods, but never at what locations, novelty increases or decreases and is supposed to represent a model of history's most important events. The original publication for his view remains to be tracked down. 
The following are related quotes:
“The five base economic units are: energy, extropy, space, time and sentience.”— Matt Frohlich (2015), on transhumanism (Ѻ), Jul 16
● Anti-entropy difficulties
1. (a) Extropy - Journal of Transhumanism Solutions (see: History section) - Extropy Institute.
(b) T.O. Morrow (Tom Bell) - Articles and c.v. (AOL Members Page)
2. (a) Foster, Thomas. (2005). The Souls of Cyberfolk: Posthumanism as a Vernacular Theory, (pg. 15). University of Minnesota Press.
(b) Extropy journal history: the printed journal Extropy: Vaccine For Future Shock, started by Max More and Tom Bell, debuted in August 1988 with only fifty copies of the first issue. The title later became Extropy: Journal of Transhumanist Thought, and a total of seventeen issues were published. In November 1997, the journal moved to the Internet as Extropy Online, where it continued to publish articles for three years. After a year of dormancy, it returned to the Web in February 2002 as its current form, Extropy: Journal of Transhumanist Solutions.
3. Ullis, Karlis (1999). Age Right - Turn Back the Clock with a Proven Antiaging Program, (section: "Human Thermodynamics", pg. 34-36, "extropy", pg 36). New York: Simon & Schuster.
4. Ekström, Karin M. and Brembeck, Helene. (2004). Elusive Consumption (pg. 190). Berg Publisher.
5. First Extropy ad - (T.0. Morrow, '89-'99)
6. What is Extropy? - MaxMore.com.
7. (a) What is Extropy? (Extropians FAQs) – Web.Archive.org.
(b) Email communicate from Libb Thims to Tom Bell, 4 May 2010.
8. Terence McKenna – Wikipedia.
9. (a) Author. (1967). “Article” (Overstreet, pg. 229; extropy, pg. 229), Physis, Vol. 9-10.
(b) Kragh, Helge and Weininger, Stephen J. (1996). “Sooner Science than Confusion: the Tortuous Entry of Entropy into Chemist” (abs), Historical Studies in the Physical and Biological Sciences, 27(1): 91-130.
● Extropy - Wikipedia.
● Max More's (philosophical) principles of extropy - Extropy Institute.