Gibbs entropy from entanglement in electric quenches

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.

Automated summary

In quantum electrodynamics with charged fermions, a background electric field leads to the chiral anomaly, creating a chirally imbalanced state of fermions through entangled pairs production. The statistical Gibbs entropy associated with these pairs is found to be equal to the entropy of entanglement between right-moving particles and left-moving antiparticles. It is observed that short pulses, such as those from high energy collisions, result in an approximately thermal distribution for the produced particles.