Entropy production associated with photon emission event

Consider a generic N-degree-of-freedom quantum system with equally spaced energy levels ($Delta E = hbar w$) described by the Hamiltonian $H=sum_{n=0}^{N-1} nhbar w|nrangle langle n |$. This quantum system is coupled to a photon field at background temperature $T$. We consider the top-level $|N-1rangle$ to be unstable, meaning that it can decay to the ground state $|0rangle$ by emission of a photon with energy $E_{rm photon}=(N-1)hbar w$. We assume that the reverse process of this decay, being the absorption of a photon with energy $E_{rm photon}$ causing the transition $|0rangle rightarrow |N-1rangle$, is negligible (occurs with negligible probability) due to the background temperature $T$ satisfying $k_{rm B}T ll E_{rm photon}$.

We are concerned with a situation where the system is prepared in a generic mixed state $rho = sum_{n=0}^{N-1}p_{n}|nrangle langle n|$, where $p_{n}$ denotes the occupation probability of the $n$th level. Given that we observe/detect the emission of a photon with energy $E_{rm photon}$, what is the change in entropy of the total system (which we regard as closed) $Delta S_{rm tot}$ composed of the N-degree-of-freedom quantum system and the photon field and a measurement apparatus, as well as the change in entropy of the individual subsystems ($Delta S_{rm system}$, $Delta S_{rm photon field}$, and $Delta S_{rm app}$)?

I am quite certain that $Delta S_{rm system}=H_{rm VN}(|0rangle langle 0|)-H_{rm VN}(rho) = -H_{rm VN}(rho)$, where $H_{rm VN}$ denotes the von Neumann entropy $H_{rm VN}(rho) = -sum_{n=0}^{N-1}p_{n}log(p_{n})$ which vanishes for any pure state, thus $H_{rm VN}(|0rangle langle 0|)=0$. However, I am uncertain about $Delta S_{rm photon field}$ and $Delta S_{rm app}$. What about the correlations between the different subsystems?