Planckian bound on the local equilibration time

TL;DR

This work proves a universal Planckian lower bound on the local equilibration time $\tau_{eq}$, defined as the onset of hydrodynamics for conserved densities, by exploiting the analytic structure of real-time thermal correlators. Using a MSS-inspired bound on the rate of change of a regulated two-sided correlator and hydrodynamic tails, they derive $\tau_{eq} \geq \alpha\frac{\hbar}{T}$ with $\alpha$ depending on dimensionality and the type of hydrodynamic behavior (e.g., diffusion gives $\alpha=\frac{d}{2\pi}$). The results are interpreted through an effective field theory of fluctuating hydrodynamics, clarifying how loop and derivative corrections relate to the Planckian scale and showing that analyticity constrains even potential “super-Planckian” EFTs. The bounds extend to sub/superdiffusion and sound modes, with caveats for exponential decays and Liouvillian gaps, and have potential implications for strange metals and transport, linking Planckian thermalization to diffusivity and resistivity through causality. Overall, the paper provides a robust, locality-based framework tying rapid thermalization to fundamental quantum bounds, applicable across generic local quantum many-body systems.

Abstract

The local equilibration time $τ_{\rm eq}$ of quantum many-body systems is conjectured to be bounded below by the Planckian time $\hbar /T$. We formalize this conjecture by defining $τ_{\rm eq}$ as the time scale at which a hydrodynamic description emerges for conserved densities. Drawing on analytic properties of real time thermal correlators, we establish a rigorous lower bound $τ_{\rm eq} \geq α\hbar /T$ on the onset of hydrodynamic behavior in a `regulated' thermal two-point function. The dimensionless coefficient $α$ depends only on dimensionality and the type of hydrodynamic or diffusive behavior that emerges, and is independent of the thermalization mechanism or other microscopic details. This bound applies universally to local quantum many-body systems, with or without a quasiparticle description, including in the presence of inelastic scattering.

Figures (2)

• Figure 1: Top: the local equilibration time $\tau_{\rm eq}$ can be defined as the time beyond which correlation functions (orange) agree with hydrodynamic predictions (blue dashed). Bottom: analyticity of the two-sided correlator $F(t) = \Tr [\sqrt{\rho}n(t)\sqrt{\rho}n]$ implies that its derivative is bounded $\beta |F'|/F \leq \pi$ (gray forbidden region). Hydrodynamic behavior cannot onset too early or it would violate that bound.
• Figure 2: Illustration of the bound $\frac{d}{2} \leq \frac{\pi t}{\beta} \coth (\frac{\pi}{\beta}(t-t_0))$ for different values of $t_0$. Dashed lines indicate bounds on $\tau_{\rm eq}$ at each value of $t_0$. Taking the weakest such bound (black) gives $\tau_{\rm eq} \geq t_c$.