@MattHanson Thank you! Your answer suggests that the second law is really about macrostates and the fact that a system tends towards a macrostate that maximizes the entropy. But I don't see how this also captures the idea that the microstates follow a probability distribution that is as uniform as possible.

@TobiasFünke It seems I should read Jaynes' work right away.

@JonCuster I had always thought of statistical mechanics as more fundamental so shouldn't the laws of thermodynamics be expressed using it?

Thank you! Why is a Grassmann-even supernumber having a nilpotent soul a bad thing?

Thanks for all the help!

Thank you! When you say that Grassmann-ness is omitted in the discussion of spinor Lorentz transformation, does this mean that the Grassmann algebra is given a trivial representation of the Lorentz group?

@Qmechanic Thanks for catching that, I have edited my post so $n$ only have one meaning.

@Qmechanic I am not following any particular reference. I recall reading in a few places that in quantum field theory the Grassmann algebra must be infinite dimensional. I could try to find some of these references if that would help improve the question.

@Qmechanic I am not following any particular reference. Would you like me to find a reference for anything in my post?

@TobiasFünke In Schroeder's An Introduction to Thermal Physics he says: "In an isolated system in thermal equilibrium, all accessible microstates are equally probable". This is what was throwing me off, but I was overlooking the "in an isolated system" part which implies the microcanonical ensemble. Now I see where I was going wrong. I'm still not sure I fully appreciate why nature chooses chooses the distribution that is as uniform as possible, but I'll continue studying and reading the references you gave for that. Thanks for all the help!