I think the shortest way of explaining the ground-breaking contribution of  Nobel prize winning physicist Ilya Prigogine is to quote from Fritjof Capra's "The Web of Life," with my additional comments in brackets and at the end.

"In open systems, Bertalanffy [seminal author of "General System Theory"] speculated, entropy (or disorder) may decrease, and the second law of thermodynamics may not apply. He postulated that classical science would have to be complemented by a new thermodynamics of open systems. ...It was the great achievement of Ilya Prigogine, who used a new mathematics to reevaluate the second law by radically rethinking traditional scientific views of order and disorder, which enabled him to resolve unambiguously the two contradictory nineteenth-century views of evolution.

"In open systems, Bertalanffy [seminal author of "General System Theory"] speculated, entropy (or disorder) may decrease, and the second law of thermodynamics may not apply. He postulated that classical science would have to be complemented by a new thermodynamics of open systems. ...It was the great achievement of [Nobel prize winning] Ilya Prigogine, who used a new mathematics to reevaluate the second law by radically rethinking traditional scientific views of order and disorder, which enabled him to resolve unambiguously the two contradictory nineteenth-century views of evolution.

Bertalanffy correctly identified the characteristics of the steady state as those of the process of metabolism, which led him to postulate self-regulation as another key property of open systems. This idea was refined by Prigogine thirty years later in terms of the self-organization of "dissipative structures." "

Prigogine was the author (along with co-author Isabelle Stengers) of some excellent books, such as Order Out of Chaos, From Being to Becoming, and The End of Certainty. Prigogine has been the key inspiration for non-equilibrium thermodynamics (N.E.T.), currently gaining scientific support, and popularized in the book Into the Cool by Schneider and Sagan.
http://www.press.uchicago.edu/Misc/Chicago/739368.html

Howard T. Odum was a pioneer thinker, a key voice in the development of "systems ecology."  He was able to connect the dots between Energy, Ecology, and Economics, and formed the foundation for the field of "Biophysical Economics," which takes Ecological Economics to the next logical step. He was also a foundational influence on some of the underlying concepts of Permaculture. The books Odum wriote for general audiences are highly recommended: "Energy Basis for Man and Nature" (1976) and "A Prosperous Way Down: Principles and Policies" (2001).

Another of his powerfully influential books was "Environment, Power and Society: The Hierarchy of Energy," first published in 1971. A new edition was completed by some of his top students after Odum passed away from brain cancer in 2002: "Environment, Power, and Society for the Twenty-First Century" (2007).

From the forward: "Most important, however, Environment, Power, and Society helped many of us to understand the interrelationships of energy and environment and their importance to the well-being of humanity and the planet. His goal was always to gain understanding through unifying rather than dissecting, through aggegating rather than disaggregating. In his life he was constantly engaged in a zealous search for truth and understanding regardless of where that search carried him. H.T. often wrote of his desire to simplify to increase understanding...

[Odum wrote,] "If the bewildering complexity of human knowledge developed in the twentieth century is to be retained and well used, unifying concepts are needed to consolidate the understanding of systems of many kinds and to simplify the teaching of general principles" (Odum, Ecological and General Systems: An Introduction to Systems Ecology, 1994).

Classic H.T. Odum is condensed in the attached article first published in 1973: "Energy, Ecology, and Economics."  Re-published the following year in 1974 in Mother Earth News to great acclaim: "We had only to glance at this extraordinary document to realize that the paper (originally written at the request of the Royal Swedish Academy of Sciences) is one of the most concise — yet most sweeping — examinations yet made of the real problems of the world. Read it and see for yourself."
Energy%2C%20Ecology%2C%20and%20Economics.pdf

The work of Peter Pogany has been discussed numerous times in this thread. I've put together a compilation document that summarizes, in his own words, Pogany's thoughts on the thermodynamic unfolding of recent world history in the sub-epochs he calls Global System 0, Global System 1, Global System 2, and Global System 3. See attachment.

The heart of the document, World History as the Synoptic Narrative of Thermodynamic Unfolding, came originally as part of a 2010 paper called “What’s Wrong with the World? Rationality! A critique of economic an....” It was later published as Appendix B in the book “Havoc: Thy Name is Twenty First Century,” (2015). This paper is based mostly on the last edit printed in “Havoc,” with some additions that come from the original 2010 paper…and various additional quotes at the end.

The potential third global system that Pogany projected as a possibility was thus characterized:

"Long-term world equilibrium -- GS3

The thermodynamic interpretation of global history predicts a halt to population and economic expansion for purely physical reasons. This general condition requires a new global system: GS3 – two-level economy/strong multilateralism/mostly government money (maximum reserve banking).

Legally binding international agreements on the use of nonrenewable energy and material resources, as well as on harmful emissions, would enlarge the government’s role in economic affairs since administrative methods would be needed to ensure national compliance with globally determined goals. The implied strong multilateralism would split national economies (hence, the world economy) into a free-market and a public authority-dominated sector. While carrying on the best traditions of constructive entrepreneurship, businesses in the first domain would bid for resources and emission rights; joint private-public ownership would prevail in the second one. The state’s substantial holding of private shares would eliminate most, if not all, income taxation.

The monetary system would be based on a global currency issued by the global central bank. The world currency would combine the discipline GS1’s gold standard vouchsafed and the flexibility GS2’s fiat money has provided (without the fractional reserve system, which, as will become obvious during the first half of the 21st century, is wholly incompatible with any consciously pursued economic steady state.) Much along the lines proposed by Keynes at the 1944 Bretton Woods conference, an international clearing house would keep cross-border trade in equilibrium.

Maximum bank reserves would restrict the ability of banks to extend loans. Just as under the prevailing minimum reserve system, some banks in some instances may keep no reserves at all; under the maximum reserve system some banks in some instances might be required to keep 100 percent reserves. While such an arrangement may not eliminate the creation of money through debt, it would certainly change its nature. The consent of depositors would be required to make loans, making financial intermediation once again the modest helper that draws together scattered household savings in order to place them into the hands of bona fide entrepreneurs. “Enterprise,” in the Keynesian sense, would squeeze out “speculation.”

The economic role of grass roots communities would increase significantly."

See the attachment for the complete summary paper. 

Michel Bauwens and Jose Ramos also have a very good short summary of Peter Pogany here:
https://wiki.p2pfoundation.net/Pulsation_of_the_Commons#Pogany:_the...

Also see my Peter Pogany page at my website:
https://integralpermaculture.wordpress.com/peter-pogany/