# Hod's universal relaxation bound From quantum information theory, there is a bound on the maximum rate at which information may be transmitted by a signal of duration $\tau$: $ \dot{I}_{\max }=\pi \Delta \mathcal{E} / \hbar \ln 2. $ For BHs, [[Hod2006]] argues that this implies an upper bound on the entropy change: $ \frac{\Delta S}{\tau} \leq \pi \Delta \mathcal{E} / \hbar $ which implies that $ \tau_{\min }=\hbar / \pi T $ saying that a thermodynamic system has at least one perturbation mode whose relaxation time is $\tau_\text{min}$. ## Relation to [[0430 Holographic shear viscosity|shear viscosity]] - [[Hod2009Essay]] derives [[0430 Holographic shear viscosity]] bound from the universal relaxation bound ## Relation to [[0208 Strong cosmic censorship|strong cosmic censorship]] - see recent paper [[KonoplyaZhidenko2022]][](https://arxiv.org/pdf/2210.04314.pdf) and refs therein ## Refs - OG: [[Hod2006]] - [[Hod2007]]: extremal limit - [[Hod2008]]: Kerr-Newman - [[Hod2009Essay]]