> Lines 1, 2 and 3, together, uniquely determine special and general relativity, cosmology, the Hilbert Lagrangian and Einstein's field equations, as told here. This is a huge exaggeration. For example 1 says "W=∫L" but L is never defined. The definition of L hides a lot of details, in particular that each point of the universe is equivalent, so there is translation invariance that using the Noether's theorem implies…
For non-physicists: you can model a gas as a bunch of almost entirely non-interacting particles in a box. You can assume that there is some way for them to exchange energy, but you don’t need any details at all of how that works. With some care (and IMO a really fascinating series of arguments) you can derive the ideal gas law and a whole lot of useful thermodynamics. As a first hack at reducing it to one sentence, I might try “at equilibrium, each unit of phase space (or each discrete microstate in a discrete system) is equally likely.”
(I personally find statistical mechanics much more intuitive than classical thermodynamics. I have always felt like E, H, F, and G are mathematically correct quantities that come from manipulating partial derivatives but that they mostly lack intuitive value. The quality of the average thermodynamics textbook doesn’t help.)