Entropy of Schwinger pair production in time-dependent Sauter pulse electric field

Abstract We investigate entropy of electron-positron pair production in time-dependent Sauter pulse electric field. This work compares the pair production entropy in the longitudinal-momentum-only approximation and the full momentum case, and assesses the impact of transverse momentum components. We further examine three types of entropy, one is the usual entanglement entropy $S_{\text{E}}$, the other two extensions are thermal distribution entropy $S_{\text{Th}}$, and that with the chemical potential correction, $S_{\text{Th,CP}}$. For short pulse, $S_{\text{E}}$ is higher than $S_{\text{Th}}$ and vice versa for long pulse. The chemical potential causes the single-particle average thermal distribution entropy $\frac{S_{\text{Th,CP}}}{N}$ to exhibit non-monotonic behavior, similar to the single-particle average entanglement entropy $\frac{S_{\text{E}}}{N}$ in the short-pulse range. In the full momentum case, we calculate the thermal distribution entropy $S_{\text{Th, U}}$ via introducing the Unruh temperature as the local effective temperature. We find that both $S_{\text{Th, U}}$ and $S_{\text{E}}$ saturate asymptotically to the constant while the former has a larger asymptotic value. The results reveal a distinct crossover behavior: the entanglement entropy exceeds the thermal-distribution entropy in the short-pulse regime, while the opposite holds true for long pulses.