Thermalization, Viscosity and the Averaged Null Energy Condition

TL;DR

This paper investigates how the averaged null energy condition constrains thermal states in relativistic quantum field theories, linking thermalization length and viscosity to potential violations, with implications for systems like quark-gluon plasma.

Contribution

It introduces the concept of thermalization length in quantum field theories and connects it to energy condition violations via the eigenstate thermalization hypothesis.

Findings

Thermal fluctuations can violate the averaged null energy condition under certain conditions.

Bounds on thermalization length and viscosity are derived, especially relevant for large N systems.

Results have implications for understanding real-world systems like the quark-gluon plasma.

Abstract

We explore the implications of the averaged null energy condition for thermal states of relativistic quantum field theories. A key property of such thermal states is the thermalization length. This lengthscale generalizes the notion of a mean free path beyond weak coupling, and allows finite size regions to independently thermalize. Using the eigenstate thermalization hypothesis, we show that thermal fluctuations in finite size `fireballs' can produce states that violate the averaged null energy condition if the thermalization length is too short or if the shear viscosity is too large. These bounds become very weak with a large number N of degrees of freedom but can constrain real-world systems, such as the quark-gluon plasma.