It would be wrong to think that \(p_x\) is proportional to \(E=mv^2\) that the \(E\) like an ideal gas follows a Maxwell–Boltzmann distribution. And so, \(p_x\) follows a Maxwell–Boltzmann distribution.
It is more correct to think of entanglement as an event that happens for a random number of times, \(n_{\lambda\,e\_x}\) over a fix interval when all the particles has light speed \(c\). That on each encounter a quantum of energy is exchanged and over the fixed internal,
\(p_x=\cfrac{n_{\lambda\,e\_x}.\Delta Q}{mc^2}\)
\(p=\cfrac{n_{\lambda\,e}.\Delta Q}{mc^2}=\cfrac{1}{2c}\) ---(*), from "Emmy NoEther" dated 6 Jul 2015.
where \(\Delta Q\) is the packet of energy exchanged on each encounter and \(n_{\lambda\,e}\) is the event rate when the interval is fixed at one second. \(n_{\lambda\,e}\) is estimated as the average of \(n_{\lambda\,e\_x}\) over a large number of fixed intervals. \(p\) and \(p_x\) are now observed over the fixed interval.
It is an assumption that a discrete quantum of energy is exchanged on each encounter. Entanglement is a quantum phenomenon when particles behave as waves, it is not an assumption that the particles have light speed, \(c\).
Previously, a large population of particles presents an average fractional entanglement, \(p\) for all time. Here, one particle is observed over a fixed time interval and it experiences \(n_{\lambda\,e\_x}\) entanglement encounters over the time period. Averaged over many fixed intervals, we estimate \(n_{\lambda\,e}\), which is related to \(p\) by equation (*). \(p\) is now qualified as fractional entanglement per time interval. Here, entanglement results in a fractional loss of energy of amount \(mc^2\) per time interval.
But not everyone loss energy; we choose to focus on the one in the entangled pair receiving (external) energy input, a fraction of which is loss per second; when the fixed observation interval is one second.
Peck was promoting Data Plans door to door...
Note: \(p_{\small{Q}}=\cfrac{\Delta Q}{mc^2}\) shall be called the quantum fraction, where \(\Delta Q\) is the packet of energy exchanged on each entanglement encounter.
\(n\) packet loss is considered \(n\) consecutive encounters. Within each fixed interval it does not matter how long each encounter takes, as long as it is counted.
This way the actual mechanisms of entanglement can be set aside, all we need to know is that entanglement occurs and how many times it occurred over a fixed interval.
