Landauer's princple for Fermionic field in one dimensional bag

We study the Landauer's principle of an Unruh-DeWitt detector linearly coupled to Dirac field in $1 + 1$ dimensional cavity. When the initial state of the field is vacuum, we obtain the heat transfer and von Neumann entropy change perturbatively. For the thermal state, the heat transfer and entropy change are approximately obtained in the case where the interaction time is long enough and the Unruh-DeWitt detector is in resonance with one of the field mode. Compared to the real scalar field, we find the results of vacuum initial state differs solely from the helicity of the Dirac field and the distinguishablity of fermion and anti-fermion comes into play when the initial state is thermal. We also point out that the results for massless fermionic field can be obtained by taking the particle $m\rightarrow 0$. We find that in both cases satisfy Landauer's principle.