Entropy, Kalam, and First Cause

[Anomalocaris]

If quantum mechanics assert variable values within the universe must be discrete, does that not mean some minimum possible differences in entropy must exist and would be defined by difference in entropy between two states in which there is the least possible number and magnitude of differences in variable which would result in some difference in entropy?

Well... QM does not assert that all variable values must be discrete. The energy levels of a hydrogen atom are only discrete because the electrons are confined in a small finite space. Very roughly speaking, the Energy increment goes like

Delta E ~ h*c / Size

where h is Planck's constant. If the universe has finite size R, there will be an energy quantization of Delta E ~ h*c/R, but you'd never see it.

Wait, that's the relativistic formula. For low energy particles, it's

Delta E/sqrt(E) ~ sqrt(2/m) h/R

It seems to me all values are some composite of units of time, length, and mass. If time, length and mass are discrete, does that not imply all possible physical values must also ultimately be discrete?