Robert E. Ulanowicz, a theoretical ecologist and philosopher, was a professor of theoretical ecology at the University of Maryland Center for Environmental Science, and now is in the Department of Biology at the University of Florida.

In his 1997 book Ecology, The Ascendent Perspective, Ulanowicz introduces an index, or measure, of processes in ecology describable as constraints in flow networks between "compartments." He writes...

[W]e define as the most indeterminate network of flows one in which each compartment contributes to and receives from all compartments in proportion to the fraction of the total system throughput [later TST]. The amount by which any given flow deviates from maximal indeterminacy defines its contribution to the information of the network under study...

Summing all the contributions [from each flow] results in what is called the average mutual information (AMI) of the flow structure. AMI measures the average amount of constraint upon an ordinary quantum of currency in passing from one compartment to the next...

The resulting product of TST times the network AMI we call the "ascendency" of the system...

In the absence of overwhelming external disturbances, living systems exhibit a natural propensity to increase in ascendency.

In a recent work, Process Ecology: Making Room for Creation, Ulanowicz writes...

The laws of physics, because they are cast in terms of homogeneous variables, fall short of determining outcomes in heterogeneous biological systems that are capable of an immense number of combinatoric changes. The universal laws are not violated and they continue to constrain, but specification of results is accomplished instead by stable configurations of processes that develop in a nonrandom, but indeterminate manner. The indeterminacy of physical laws puts an end to Deist speculations and necessitates an alternative to the mechanical-reductionistic metaphor for nature. An antithetical Heraclitan metaphysics, called ‘Process Ecology,’ entails a dialectic between centripetal creation and centrifugal decay in which nature, humanity and the Divine can all potentially participate. The dialectic can be quantified and tracked using information measures applied to networks of processes to allow for the statement and testing of falsifiable hypotheses. Creation no longer appears as an emergent enigma, but rather as a core phenomenon of Process Ecology that allows for free will, Divine intervention, intercessory prayer and a necessary tolerance for petty evil. No longer is ‘heat death’ the inevitable and only endpoint of the cosmos. Rather, the course of the universe may include as well the production of ‘perpetual harmonies’ akin to Teilhard’s ‘Omega Point.’

In the dialogue between science and religion many exchanges between physicists and theologians are aimed at papering over the yawning gap between their respective metaphysics, as though it does not exist. While biologists do enter the conversation, most do so as physicalists, believing that all sciences are derivative of physics. Physicists, of course, are delighted to encourage this belief—witness the opinion shared by Nobel Laureates Murray Gell-Mann and David Gross, who maintain that all causality originates from below and that there is nothing ‘down there’ but the laws of physics (Kauffman 2008).

Such nihilism is the trademark of those who deny the authenticity of anything theological. Encouraged by the absence of any violations of the four force laws of physics (strong and weak nuclear forces, electromagnetism and gravity), Carl Sagan and Hawking (1988) sought to seize the entire domain of metaphysics with their belief that ‘There is nothing left for a Creator to do.’ So cowed are many believers by the power of physics and the other sciences that even a believer like Hefner (2000) came to doubt that miracles can happen, lamenting that God ‘just doesn’t have enough “wiggle room”.’ Many who still pray have abandoned intercessory prayer in the Neo-Deist belief that God cannot act in a world totally ruled by the laws of science. Truly, a metaphysical chasm persists between physics and theology.

In his 2009 book, A Third Window; Natural Life Beyond Newton and Darwin, Ulanowicz reviews "average mutual information (AMI)"

AMI is a measure of how well organized or determinate a configuration of relationships appears, as will be elaborated in thee chapters that follow. The mathematical form of the mutual information resembled a familiar quantity from thermodynamics called the Gibbs-Helmholtz free energy, which was consructed to measure how much work a system could possibly perform. The problem was that the AMI, coming as it did from information theory, carried no physical dimensions; it could not indicate the size of the system to which it was being applied. In order to maintain the parallel with thermodyamics, I needed to impart the dimensions of work to the AMI. Perhaps the simplest way of doing this was to scale (multiply) the AMI by the total activity (sum of all flows [TST]) inherent in the ecosystem.

The resulting product I called the system's ascendency because it represented the coherent power a system could bring to bear in ordering itself and the world around it. Over the course of the following two weeks, I tested how well the measure could mimic various facets of organization. I was excited to discover that the index nicely encapsulated almost all the major attributes that Eugene Odum (1969) had used to characterize more "mature" or developed ecosystems. That is, increasing ascendency appeared to descnbe quantitatively both the growth and development of ecosystems. As it turned out, 1 finally had formulated a phenomenological statement around which to configure my accumulated renegade observations.

I soon became aware of my inability to devise any explanation by which ecosystem development in the guise of increasing ascendency could be explained fully in terms of the actions of its individual parts. It gradually dawned upon me that the tenet of increasing ascendency, like the second law before it, directly challenges the prevailing mechanical view of the world. My readings in thermodynamics had alerted me to the fact that, in any confrontation between phenomenology and theory, theory remains at risk, until it can be otherwise supported. Having not yet formulated a coherent theory to elucidate the rise of ascendency, I acted conservatively by presenting my discovery primarily in phenomenological terms. Thus, my first book, Growth and Development, carried the subtitle Ecosystems Phenomenology (Ulanowicz 1986). ln that volume, I also elaborated a number of ancillary mathematical methods useful in analyzing ecosystem networks.

In his 2023 book, The First Incarnation:Hope in Reality, Ulanowicz returns to the relationship between science and religion.

It is my hope that by introducing significant new discoveries from ecosystems theory I can provide a new layer of material for expanded conversations on issues between science and religion. But first l will devote myself to deconstruction of the widespread belief that all of reality issues from and comes down to the fundamental laws of physics, otherwise known as obligate physical reductionism. I do not believe that the physical laws are violated, only that their ability to determine higher level phenomena is limited. They continue to constrain, but they lose their powers to determine specific outcomes in complex systems.

Demonstrating the semi-autonomy of larger systems from microscopic antecedents opens up rational consideration of numerous transcendental questions, that occupy those studying the relationship between science and religion, such as the existence of free will, the possibility of Divine intervention and miracles, the efficacy of intercessory prayer, the existence of direction in evolution, the broader conception of aleatoric events beyond blind chance, and an eschatological end of the universe, other than a meaningless "heat death."