What is physics explanation for minimum sink rate airspeed?
From first principle, assuming the airplane is a point mass, no wind, small angle of attack, and thrust acts in-line with drag:

$$T-D-W\sin \gamma=m\dot{V}$$

where $T$ is thrust, $D$ is drag, $\gamma$ is angle of climb, $m$ is mass of the airplane, $W=mg$ is weight, $V$ is airspeed/forward speed (assuming no wind).

In a total power off scenario, $T=0$, and assuming steady-state, $\dot{V}=0$:

$$\sin \gamma = -\frac{D}{W}$$

The rate of climb ($\dot{z}$), which is the negative of sink rate, is related to angle of climb by: $\dot{z}=V\sin \gamma$. Therefore, we have:

$$\dot{z}=-\frac{DV}{W}=-\frac{P_R}{W}$$

Therefore, for minimum rate of descent, we would like the minimum power required ($P_R$).

Note: for minimum glide slope, it corresponds to $L/D_{max}$, but not for minimum rate of descent.