Which stellar properties can we describe as "first principles" in which we can derive the rest? Mass, size, temperature, luminosity, chemical composition, the initial abundance of the molecular cloud, distance, brightness, age, and evolutionary cycle can all be used to characterize a star. A star's brightness is dependent upon its distance and luminosity, so brightness is not a &quot;first principle&quot;; however, there are some properties that seem less obvious in determining their dependencies. For example, chemical composition and temperature seem to be at a constant interplay. Does one always inform the other? Chemical composition and mass influence a star's evolutionary cycle, so it's evolution through the HR diagram is also not a first principle (from my understanding).
For fun, if we wanted to describe a star in the most simplistic way possible, which properties would we need to know? My assumption would be the initial chemical composition when the star was made and its initial mass. If we wanted to know the star's brightness for observational purposes we would also need to know the distance, but this isn't a fundamental property of the star. In other words, what are the basic properties we need to know to extrapolate the rest? I'm, betting on mass and initial chemical composition, but am unsure about temperature. We can throw in distance for observing properties but I was mainly using this as an example.
Starting from a protostar, one would hope to be able to predict everything about its future development if we knew its initial mass, chemical composition and angular momentum.
Mass is fundamental because it determines how much fuel the star will have and the pressure at its core. Composition is key because among other things it determines the opacity of the stellar material. Angular momentum is important because rotation can alter the structure of the star, if fast enough, and can also enhance internal chemical mixing.
Of course extrinsic factors like interactions are also possible, so the properties of any companions are also fundamental, as might be the birth environment that can do things like hasten the dispersal of circumstellar material from a protostar.
If you are talking about figuring out the past and future of a star observed midway through its life, then in addition to the above, we may need to know how the chemical composition varies with depth inside the star, since it will not be uniform.