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

Zhi-Hang Yao, Hong-Hao Fan, Lie-Juan Li, Hai-Bo Sang, Bai-Song Xie

TL;DR

The paper studies entropy production during electron-positron pair creation in a time-dependent Sauter pulse, comparing entanglement entropy in 1+1 longitudinal momentum with full momentum treatment and introducing several thermal-like entropies, including chemical-potential corrections and Unruh-based temperatures. It derives analytic Bogoliubov-based expressions for entanglement entropies, analyzes momentum distributions that exhibit thermal-like behavior, and quantifies thermal entropies using effective temperatures; it also reveals circumstances under which entanglement and thermal entropies coincide or diverge. Key findings show distinct time evolution for S_E,L and S_E,F, asymptotic saturation for both, and nuanced relationships among S_E, S_Th, and S_Th,CP depending on pulse width. The work provides a framework linking quantum entanglement and thermodynamic entropy in non-equilibrium QED, showing how effective and Unruh temperatures can capture nonperturbative, time-dependent entropy generation and guiding future refinements with momentum- and time-dependent thermodynamic parameters.

Abstract

We investigate entropy of electron-positron pair production in time-dependent Sauter pulse electric field. Both cases of pair longitudinal momentum only and full momentum consideration are examined. 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 presented in this study reveals that the different entropies have some delicate relationships among them.

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

TL;DR

The paper studies entropy production during electron-positron pair creation in a time-dependent Sauter pulse, comparing entanglement entropy in 1+1 longitudinal momentum with full momentum treatment and introducing several thermal-like entropies, including chemical-potential corrections and Unruh-based temperatures. It derives analytic Bogoliubov-based expressions for entanglement entropies, analyzes momentum distributions that exhibit thermal-like behavior, and quantifies thermal entropies using effective temperatures; it also reveals circumstances under which entanglement and thermal entropies coincide or diverge. Key findings show distinct time evolution for S_E,L and S_E,F, asymptotic saturation for both, and nuanced relationships among S_E, S_Th, and S_Th,CP depending on pulse width. The work provides a framework linking quantum entanglement and thermodynamic entropy in non-equilibrium QED, showing how effective and Unruh temperatures can capture nonperturbative, time-dependent entropy generation and guiding future refinements with momentum- and time-dependent thermodynamic parameters.

Abstract

We investigate entropy of electron-positron pair production in time-dependent Sauter pulse electric field. Both cases of pair longitudinal momentum only and full momentum consideration are examined. We further examine three types of entropy, one is the usual entanglement entropy , the other two extensions are thermal distribution entropy , and that with the chemical potential correction, . For short pulse, is higher than and vice versa for long pulse. The chemical potential causes the single-particle average thermal distribution entropy to exhibit non-monotonic behavior, similar to the single-particle average entanglement entropy in the short-pulse range. In the full momentum case, we calculate the thermal distribution entropy via introducing the Unruh temperature as the local effective temperature. We find that both and saturate asymptotically to the constant while the former has a larger asymptotic value. The results presented in this study reveals that the different entropies have some delicate relationships among them.

Paper Structure

This paper contains 6 sections, 15 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Entropies of EPP Production in Sauter Pulse electric field
  3. Entanglement Entropy $S_{\text{E,L}}$ and $S_{\text{E,F}}$
  4. The Momentum Dependence of EPP Production and the Thermal-like Behavior
  5. Thermal Distribution Entropies $S_{\text{Th,B}}$, $S_{\text{Th,F-D}}$ and $S_{\text{Th,CP}}$
  6. Conclusion and Discussion

Figures (3)

  • Figure 1: Comparison of the time-dependent relationships of entanglement entropy between the longitudinal momentum case and the full momentum case.
  • Figure 2: Comparison of entropis. The blue, red, yellow, and purple curves correspond to $\frac{S_{\text{E,L}}}{N}$, $\frac{S_{\text{Th,B}}}{N}$, $\frac{S_{\text{Th,F-D}}}{N}$, and $\frac{S_{\text{Th,CP}}}{N}$. We also reproduce the results of Ref. 21 for the blue and red curves.
  • Figure 3: Comparison of $S_{\text{Th,U}}(t)$ and $S_{\text{E,F}}(t)$.