The interview of Tim Garrett above may be of some interest, although it’s been around a while.
Here is a link to a 2013 paper: Thermodynamics of long-run economic innovation and growth. https://arxiv.org/pdf/1306.3554v1.pdf#page=23&zoom=auto,-73,715
There is a lot of mathematics in this paper but also good written interpretations.
From the paper we have this figure (pg. 23) in which the x-axis represents the rate of return on investment and the Y-axis the rate of technological advancement.
I believe what this shows is technological innovation pushing to the right as new tools are used to consume existing gradients more efficiently and open up new gradients if they exist. This trend is always facing the headwind of diminishing returns as each new iteration of technology becomes more expensive and provides less net profit. When innovation fails to provide any new energy/resources, then diminishing returns wins and you approach a zero return on investment and zero GDP growth. This is a time of fragility as indicated by the small box in the center. Any rate of return less than zero means technology has failed to open up any new energy vistas and decay and/or collapse commence. Seems like we’re about at the point of decay and collapse now.
It looks like technology began to fail around 1980, at least in the case of oil where production (equals consumption) overcame technologies best efforts to find more reserves. At that point we were consuming from developed legacy fields and collapse was baked into the cake. Even though it’s easily determined that future production would be curtailed even with the use of fracking technology, we continued to grow our civilization. All of those large finds from about 1935 to 1980 have been used to build endless numbers of technological cells, distribution systems and all sorts of complexity. Now the black production curve has pretty much peaked far above the annual reserve additions. Will more innovation besides fracking save us? Not likely. Return on investment is pushed towards zero. In some cases we are already experiencing negative interest rates or return on investment which will push us into decay.
These are some of Garrett’s conclusions from the paper:
“Global GDP growth requires energy consumption to grow super-exponentially, or at an accelerating rate. GDP growth is sustainable for as long as energy reserve discovery exceeds depletion.”
“When growth rates slow and rates of return approach zero, civilization becomes fragile with respect to externally forced decay. It lies along a tipping point that might easily lead to a mode of accelerating decay or collapse.”
“Innovation and collapse are two sides of the same coin. Increased internal connectivity allows for explosive growth when times are good, but also for exceptionally fast decline when times turn bad.”