In religious thermodynamics, entropological proof or 'entropy proof of God's existence' or 'entropic proof' is an entropy-based argument for the existence of god.
In 1274, Italian priest and philosopher Thomas Aquinas, in his Summa Theologica, gave his proof ex motu, which is said to be a forerunner to the entropological proof. 
In 1869, German physicist Adolf Fick, in his lecture series “The Forces of Nature in their Relationship”, gave the first outline of the entropy proof, in which he extrapolated German physicist Rudolf Clausius’ heat death theory of universal end to give what is said to be the first contour of the ‘entropy proof of God’s existence’, to argue that God must exist, because of the second law of thermodynamics; though, to note, he only stated the argument, remaining agnostic about the validity of the proof, stating something along the lines that more evidence, work, or data was needed. 
In 1910, German physicist Caspar Isenkrahe published his Energy, Entropy, and the Beginning and End of the Universe discussing his views on the possible relationship between God and entropy. 
In 1920, German philosopher Josef Schnippenkotter completed his PhD dissertation, entitled The Entropological Proof of God, in which he discussed over 320 papers (200 of which, supposedly, on entropy and god speculations) to draw the conclusion that entropy does not necessarily imply the existence of a Deity, a view summarized as follows: 
“There is no scientifically certain proof that the end and the beginning of the world, and then the existence of God, can be derived from the entropy law.”
The phrase “entropological proof” in reference to a proof for the existence based on energy dispersion dates back to at least 1898.  The points in the proof, according to English statistical thermodynamicist Peter Landsberg, is as follows: 
(a) the universe is an isolated system.
(b) isolated systems reach internal thermal equilibrium given time, after which fluctuations about this equilibrium state can take place.
(c) the universe is presently in a far-from-equilibrium state.
(d) if the universe is in a far-from-equilibrium state, it must have had a finite age and hence a beginning.
(e) this beginning must be a state of minimum entropy at which the cosmos was born.
(f) this original state was brought about by God, who also created the initial values of parameters such as initial internal energy, matter, entropy, etc., such that the initial universe was wound up, i.e. “the spring was set”, and the universe is now running down to an eventual heat death.
One of the obvious contradictions in this proof, at least according to Landsberg version, is that point (c) contradicts point (a). In other words, far-from-equilibrium systems, such as Benard cells, can only maintain such a state if they are continuously being driven by an external flux of energy or matter, and as such are open and cannot be isolated.
1. Salamucha, Jan, Świętorzecka, Kordula, and Jadacki, Jacek J. (2003). Knowledge and Faith (pgs. 98-99). Rodopi.
2. Author. (1898). Mind (pg. 139). By Mind Association, JSTOR (Organization). Publisher: Basil Blackwell.
3. Landsberg, Peter T. (1999). Seeking Ultimates: An Intuitive Guide to Physics, (pgs. 231-32). CRC Press.
4. (a) Fick, Adolf. (1869). “Die Naturkräfte in ihrer Wechselbeziehung” (“The Forces of Nature in their Relationship”), Würzburg.
(b) Kubat, Libor, and Zeman, Kiri. (1975). Entropy and Information in Science and Philosophy (pg. 237). Elsevier Scientific Pub. Co.
5. Schnippenkotter, Josef. (1920). Der Entropologische Gottesbeweis: Die Physikalische Entwicklung des Entropieprinzips, seine Philosophische und Apologetische Bedeutung (The Entropological Proof of God: the Physical Development of the Entropy Principle and its Philosophical Meaning) (quote, pg. 95). A. Marcus and E. Webers Verlag.
6. Isenkrahe, Caspar. (1910). Energie, Entropie, Weltanfang und Weltende (Energy, Entropy, and the Beginning and End of the Universe). Trier.
● Kragh, Helge. (2008). Entropic Creation: Religious Contexts of Thermodynamics and Cosmology (section: A New Proof of the Existence of God, pgs 47-51). Ashgate Publishing, Ltd.