Lets do a Bose Einstein critical temperature.

We start with something called the Riemann zeta function, the funny swirl function in the denominator of the first term. It is this:

That number at the bottom is sum n^-3/2, the first fraction, for all possible systems quantize at 3/2. That number is the largest fraction possible before the 3/2 ratio that makes a Shannon boundary. It is not a simple sum or powers because he has to allow duplicates. So the series:

e^[-log(n)*3/2] has many overlaps, log(n), n 1...Nmax not being an integer multiples. However, since we know the precision we are working toward (four digits in 3.3125) we would be free to scale up log(n) and work a power series. When we do this, we find some log(n), log(n+1)...log(n+k) are all about the same value, and we can treat them as log(N+1), and be accurate to our precision.

Einstein wants to lower the temperature sampling rate until that quant is reached, given the normal SNR for a collection of Planck motions. Since he has n particles, he can normalize that quant to each particle, because he doing only one stochastic sub channel, and does not worry about overlap of subchannels. Orthogonality is not a problem.