Thermal behavior, entanglement entropy and parton distributions

TL;DR

This paper explores how quantum entanglement of partons in high-energy collisions leads to thermalization and affects entropy, revealing a connection between parton multiplicity, energy, and entanglement entropy.

Contribution

It introduces a model linking entanglement entropy to parton distributions and shows how entropy scales with energy and multiplicity in hadronic collisions.

Findings

Entanglement entropy exceeds minimum bias entropy due to parton multiplicity distribution.

Maximum entropy occurs when all partons have equal probability.

Asymptotic entropy scales as the logarithm of the square root of the number of partons.

Abstract

The apparent thermalization of the particles produced in hadronic collisions can be obtained by quantum entanglement of the partons of the initial state once a fast hard collision is produced. The scale of the hard collision is related to the thermal temperature. As the probability distribution of these events is of the form $np(n)$, as a consequence, the von Neumann entropy is larger than in the minimum bias case. The leading contribution to this entropy comes from the logarithm of the number of partons $n$, all with equal probability, making maximal the entropy. In addition there is another contribution related to the width of the parton multiplicity. Asymptotically, the entanglement entropy becomes the logarithm of $\sqrt{n}$, indicating that the number of microstates changes with energy from $n$ to $\sqrt{n}$.