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There is an emerging trans-disciplinary field called cliodynamics which studies these ideas. There's an open access journal, Cliodynamics: The Journal of Quantitative History and Cultural Evolution, a lab in England, and an institute in New Mexico.
Cliometrics is somewhat related: it applies the ideas of economics to the study of history. It's been around somewhat longer, but has been criticised for applying neoclassical economic models to societies that operated by quite different rules.
Upvote:2
There is an esoteric field within History, more specifically, Historiography called, "MetaHistory"-(sometimes nicknamed, "Big History"). It is a subject which attempts to address the deeper meaning of historical causality and its relationship to historical time and reality.
Admittedly, I am no expert in this area of History, however, the study of historical causation is very much a type of sequential logic, that is to say, a leads to b and b leads to c, etc.
There is also a dialectical component to MetaHistory whereby every cause has an inherent effect. In other words, each cause leads to an effect, though when the effect ends, it generates a new cause. For example, if were to analyze the Vietnam War with this type of causal model, one could say that "The Domino Theory"-(which also was the justification for the Korean War), caused the the U.S. to invade Vietnam in 1964, whereby the effects of that war eventually led to the proliferation of the armed conflict into nearby Cambodia in 1970, thereby starting or causing a newer and wider conflict, etc.
If you were to sequence this pattern, you might say that "The Domino Theory" represents A, the U.S. invasion of Vietnam represents B and the Cambodian War represents C; each having an inherent and simultaneous cause and effect relationship.
MetaHistory is one of the more ambitious and highly abstract approaches towards understanding history and particularly, historiography. Although Historians and Historiographers, by their nature, are interested in the cause and effect of certain historical events, MetaHistory also attempts to understand such a process, though with greater chronological depth and philosophical awareness.
Upvote:5
You may find the field of "big history" relevant to your interests. David Christian's book Maps of Time is an excellent introduction. This work isn't as quantitatively oriented as what you are looking for, but you may still find it useful.
(As an aside, I can't resist echoing the warning tweeted by Neil DeGrass Tyson: "In science, when human behavior enters the equation, things go nonlinear. That's why Physics is easy and Sociology is hard.")