Entropy gap models
Left: a 1988 (possibly 1982) David Layzer-based entropy gap diagram, by American theoretical physicist Steven Frautschi, described as a: "schematic dependence of entropy S and maximum (equilibrium) energy Smax in the expanding universe"; such that the "gap" between the two line, Smax – S, represents the room for order in the universe, and that this is how life or intelligent order emerged in the context of the second law. [3] Right: a 2008 model version of the so-called entropy gap in the context of heat death theory, from the article “Life, Gravity and the Second Law of Thermodynamics” (figure 9), by Charles Linweaver and Chas Egan, captioned as: “The universe starts off at low entropy (not zero) due to the low level of density perturbations in the early universe—low Q and low A (e.g., [50])—where “low” means less than the maximum value Smax. At Smax all the energy density of the universe is in massless particles in equilibrium at a common temperature. Thus the universe starts off with a large entropy gap ΔS. The parameters Q and A are the observable normalizations of the primordial density fluctuations and set the initial gravitational entropy of the universe. There is no general agreement on the curve shown here. See for example Fig. 7.3 in [14] and Fig. 1.2 in [21].” [4]
In cosmological thermodynamics, entropy gap is gap between actual entropy and the maximum possible entropy, or universal thermodynamic equilibrium, created by the gravitational contraction of gas clouds into stars, in the process of universal expansion from the point of the big bang. [1]

Frautschi-Layzer diagrams
Entropy-time diagrams that show entropy gaps, in attempts to argue some point, are called Frautschi-Layzer diagrams.

In the 1988 book Evolution as Entropy, Canadian zoologist Daniel Brooks and American system ecologist Edward Wiley, employ 25 different information theory modified types of Frautschi-Layzer diagrams. [10]

Theory origin?
The "entropy gap" theory or argument seems to have originated in certain arguments in the 1975 "The Arrow of Time" by American astrophysicist David Layzer, although he does not use the actual term "entropy gap". Rather, following a near backwards convolution of information theory, statistical mechanics, arrow of time models, and big bang theory, he concludes: [7]

"The quantity of macroscopic information generated by the expansion [of the universe] is the difference between the actual value of the entropy and the theoretical maximum entropy at the mean temperature and density."

In 1982, American theoretical physicist Steven Frautschi cites the Layzer and gives a entropy gap type graph, shown adjacent, which seems to bee modeled on the above argument. American physicist Robert Doyle, likewise, in his 2003-launched InformationPhilosopher.com site, attributes the entropy gap graphical model to Layzer. [5]

The term "entropy gap" seems to have been first used in 1983 and promoted by those as physicists such as Roger Penrose, Paul Davies, and Brian Greene. Greene, for example, argues that the arrow of time points in the direction in which the entropy gap is being lessened. [2]

The following shows three entropy gap modes. Left: A 2011 summary of Layzer's 1975 entropy gap model of the universe, according to American physicist Robert Doyle. [9] Center: American physicist Victor Stenger's 2007 (possibly 2003) entropy gap model: Plot of the total entropy of the universe and the maximum entropy of the universe as a function of the radius of the universe, according to Stenger's calculations. [6] Right: A information theory modified types of Frautschi-Layzer diagram from the 1988 book Evolution as Entropy, by Canadian zoologist Daniel Brooks and American system ecologist Edward Wiley, one of 25 different ones found in their book. [10]

Entropy gap models 3
In his 1983 book God and the New Physics, American physicist Paul Davies seems to clearly dig into his gravity-driven entropy-order theory. [8] In his 1999 origin and meaning of life book The 5th Miracle, Davies devotes the second chapter to thermodynamics, concluding that:

“All life feeds off the entropy gap that gravitation has created. The ultimate source of biological information and order is gravitation.”

(add discussion)

References
1. Davies, Paul. (1999). The 5th Miracle: the Search for the Origin and Meaning of Life (section: The Entropy Gap: Gravity as the Fountainhead of Order , pgs. 49-68). Orion Productions.
2. Greene, Brian. (2004). The Fabric of the Cosmos: Space, Time, and the texture of Reality (entropy gap, pg. 525). Random House.
3. (a) Frautschi, Steven. (1982). “Entropy in an Expanding Universe”, Science, 217:593-99.
(b) Frautschi, Steven. (1988). “Entropy in an Expanding Universe”, in: Entropy, Information, and Evolution: New Perspectives on Physical and Biological Evolution (pgs. 11-22), editors: Bruce H. Weber, Bruce H., David J. Depew, and James D. Smith. MIT Press.
4. Lineweaver, Charles H. and Egan, Chas A. (2008). “Life, Gravity and the Second Law of Thermodynamics”, Physics of Life Reviews, 5(4):225-42.
5. Doyle, Bob. (2011). Free Will: the Scandal in Philosophy (pg. 11). I-Phi Press.
6. (a) Stenger, Victor J. (2003). Has Science Found God? The Latest Results in the Search for Purpose in the Universe (mathematical derivation of the curves in the plot given in Appendix C, pgs. 356-57). Prometheus books.
(b) Stenger, Victor J. (2007). God: the Failed Hypothesis: How Science Shows That God Does Not Exist (ch. 4: Cosmic Evidence, pg. 113-36). Prometheus Books.
7. Layzer, David. (1975). “The Arrow of Time”, Scientific American, 233:56-69.
8. Davies, Paul. (1983). God and the New Physics (thermodynamics, pgs. 50, 67, 171, 177, 199, 211). Simon & Schuster.
9. Doyle, Bob. (2011). Free Will: the Scandal in Philosophy (pg. 11). I-Phi Press.
10. Brooks, Daniel R. and Wilson, Edward O. (1988). Evolution as Entropy: Toward a Unified theory of Biology (pg. 368). University of Chicago Press.

Further reading
‚óŹ Al-Khalili, Jim. (1999). Black Holes, Wormholes, and Time Machines (entropy gap, pgs. 134-35). CRC Press.

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