So I'm not saying there was anything wrong with Marx developing the idea of dialectical materialism as method for analysis of history, as it was a hundred or so years before the necessary ideas would be developed and systems theory wasn't even really a thing back then. In the meantime though, we've made huge amounts of progress for describing things as complex as weather systems and ecosystems, and the capitalists are sure as hell using it in their economics research. It seems like the perfect tool to use to get an updated, more precise and accurate view of what can be predicted from the deterministic aspects of history, or at least more than a simplistic reduction of it to the struggle between two forces.
I know traditionally its the more "qualitative" branches of academia that lean sympathetic to leftist ideals. Or, at least, most of the research that incorporates leftist analysis and is applicable to the strategies and tactics of the left seems to be from those who'd be associated with "Continental" philosophy, and Postmodernism/Post-Structualism. At times, it even seems to be an air of open hostility towards the more "quantitative" methodologies. I can understand an apprehension towards the traditional old-school archetype that such can elicit. Really though, there have been some incredible breakthroughs and shifts in thinking since the 70s and 80s, and I see much potential to advance the ideas of leftism within some of these frameworks.
There are studies applying the laws of thermodynamics to capitalist economic systems will always lead to extreme concentrations of wealth, though the conclusions drawn are fairly lib:
https://www.wealthinequality.info/the-model/
I would wholeheartedly agree that chaos theory is a perfect tool for analyzing economic systems (and world/physical systems) as they are. Chaos theory clearly has revolutionary potential. An equilibriated chaotic system (one who's overall feedback loop currently keeps its large-scale organization at relative stasis) is comprised of component feedback loops on the smaller organizational scale, each governed by its own internal contradiction ruling its movement. These smaller component feedback loops can be in stasis or in motion, and their state will interact with all of those other component parts to form the larger equilibriated chaotic system. As time progresses, these component feedback loops will inevitably fall out of sync, and once positive feedback takes hold in part of the system, it spreads exponentially through the rest, until it completely removes the large scale complex system from its stasis into chaos, where we see it rapidly changing/reorganizing until the component parts find their equilibriums amongst each other, which then spreads until we have a new system in equilibrium out of the old component parts. For anyone experienced in dialectical materialism, this is a very familiar process, as it is entirely analogous to the progression of societies.