I was not saying that all the photons would chose path A. But OK. Let's analyze the extreme scenario.In either case, quantum choices were made that locally went against the global trend.
Let's assume that we've made some nice time-reversible photomultipliers and counters. So:
SP = 0;
SC = 0;
Now the only possible way of interaction with the environment is the heater. Everything else is time reversible. With the time flow entropy can only increase (it can not even stay the same!). So the only logical conclusion here is that with the time flow all the photons would chose the path A.
A completely reversible photomultiplier+counter can be replaced by a quantum harmonic oscillator. And the light source with an another oscillator with some initial energy. Here is an illustration: