Dynamical manifestation of Gibbs paradox after a quantum quench

TL;DR

This paper investigates how entanglement spreads after quantum quenches in a non-integrable quantum Ising model, revealing a phenomenon akin to the Gibbs paradox linked to new quasi-particle excitations and entropy considerations.

Contribution

It demonstrates a non-equilibrium manifestation of the Gibbs paradox in quantum systems with a complex quasi-particle spectrum, connecting entanglement dynamics to mixing entropy.

Findings

Entanglement production rate exhibits a sudden increase.

New quasi-particle excitations appear post-quench.

The phenomenon aligns with the quantum Gibbs paradox resolution.

Abstract

We study the propagation of entanglement after quantum quenches in the non-integrable para-magnetic quantum Ising spin chain. Tuning the parameters of the system, we observe a sudden increase in the entanglement production rate, which we show to be related to the appearance of new quasi-particle excitations in the post-quench spectrum. We argue that the phenomenon is the non-equilibrium version of the well-known Gibbs paradox related to mixing entropy and demonstrate that its characteristics fit the expectations derived from the quantum resolution of the paradox in systems with a non-trivial quasi-particle spectrum.