Entanglement Viscosity: from Unitarity to Irreversibility in Accelerated Frames

TL;DR

The paper addresses how quantum unitarity gives thermodynamic irreversibility for a horizon-separated subsystem by computing entanglement viscosities of Unruh radiation in Rindler space through a universal spectral representation and Kubo formulas. It expresses the shear and bulk viscosities in terms of spectral densities $c^{(2)}(\mu)$ and $c^{(0)}(\mu)$ as $\eta(\rho)= k_d \rho \int_0^{\infty} d\mu\, c^{(2)}(\mu) \mu^2 K_0(\mu \rho)$ and $\zeta(\rho)= \frac{2 k_d \rho}{(d-1)^2} \int_0^{\infty} d\mu\, c^{(0)}(\mu) \mu^2 K_0(\mu \rho)$, with positivity $c^{(0)}(\mu)\ge0$, $c^{(2)}(\mu)\ge0$ and $K_0(x)>0$ ensuring $\eta,\zeta\ge0$, thus linking entropy production to microscopic unitarity. In 4D CFTs, the viscosities are tied to the conformal anomaly, yielding $\eta = 8 a \alpha^3$ and $\zeta = 0$, with the entropy density scaling as $s \propto a \alpha^3$, and the global entanglement viscosity saturates the KSS bound $\eta_{glob}/s_{glob}=1/(4\pi)$. The results reveal a novel anomalous transport mechanism—entanglement viscosity—whose flat-space manifestation is tied to curvature-induced anomalies, with potential implications for systems undergoing extreme acceleration such as heavy-ion collisions.

Abstract

We demonstrate that the unitarity of quantum field theory, through the positivity of spectral functions, underlies thermodynamic irreversibility for a subsystem separated by a horizon, in direct analogy with the irreversibility of renormalization-group flows. To this end, we explicitly find the shear and bulk viscosities -- the entanglement viscosities -- for thermal radiation in Rindler space using the universal spectral representation. A direct consequence of the obtained general formulas is the relationship between the acceleration-induced shear viscosity in flat space and the conformal quantum anomaly in curved space, pointing to a possible novel probe of the conformal anomaly in systems with extreme acceleration. Moreover, for conformal field theories, we explicitly show that globally entanglement viscosity saturates the Kovtun-Son-Starinets bound.