Normal, Mechanical and Thermodynamic Pressure Explained

Swap PV for the work integral and enthalpy stops being a state function. A two-path counterexample, the dH = TdS + VdP derivation, and the conditions under which ΔH really equals heat.

A uniform, unchanging density can still carry transport. The current comes from the phase gradient, and a plane wave stands for a long packet, a scattering state or a particle beam, never a single normalized particle.

We check a Master Theorem construction for f^s(x) against affine maps by hand, then see where convergence and uniqueness give out.