Atomic Emission: Quantum vs Classical Radiation

Shrinking the sample space to B and dividing by P(B) look like different operations. A dice example, a uniqueness argument and a rejection-sampling proof show they are the same one.

The one-particle average of (3/2)k_B T holds for any N. What N changes is fluctuation, and how much noise you accept determines how many particles you need.

Latent heat keeps an ice bath at 0 °C, but air gaps and a thin water layer can waste that advantage. Here is how to set up the bath, and what nobody has measured yet.