Gibbs entropy from entanglement in electric quenches

TL;DR

This paper explores the relationship between Gibbs entropy and entanglement entropy in quantum electrodynamics during electric field-induced particle production, providing asymptotic expansions and analyzing time-dependent effects.

Contribution

It establishes the equivalence of Gibbs entropy and entanglement entropy for particle pairs in electric quenches and develops a resummation method for the entropy's asymptotic expansion.

Findings

Gibbs entropy equals entanglement entropy for produced pairs.

Asymptotic expansion of entanglement entropy in terms of cumulants.

Short pulses lead to approximately thermal particle distributions.

Abstract

In quantum electrodynamics with charged fermions, a background electric field is the source of the chiral anomaly which creates a chirally imbalanced state of fermions. This chiral state is realized through the production of entangled pairs of right-moving fermions and left-moving antifermions (or vice versa, depending on the orientation of the electric field). Here we show that the statistical Gibbs entropy associated with these pairs is equal to the entropy of entanglement between the right-moving particles and left-moving antiparticles. We then derive an asymptotic expansion for the entanglement entropy in terms of the cumulants of the multiplicity distribution of produced particles and explain how to re-sum this asymptotic expansion. Finally, we study the time dependence of the entanglement entropy in a specific time-dependent pulsed background electric field, the so-called "Sauter pulse", and illustrate how our resummation method works in this specific case. We also find that short pulses (such as the ones created by high energy collisions) result in an approximately thermal distribution for the produced particles.