# Beautiful Shahar Hod relax time lower bound-connecting to Third Law

1. Nov 1, 2006

### marcus

Beautiful Shahar Hod relax time lower bound---connecting to Third Law

The investigation of BHs by Shahar Hod has had a big impact Quantum Gravity. Everybody remembers the substantial hoo-hah about BH resonant frequencies, which was set off by Hod. John Baez had a piece in Nature magazine about it, I think in 2003 or 2004.

So we should be alert to anything new from Hod, and maybe it could impact QG.

This new thing is very simple and beautiful. It is a lower bound on relax time of a perturbed thermodynamic system, which he says BLACK HOLES ACHIEVE which makes them the fastest relaxing things in the world.

It has been said that the ringing of a BH is more like the ringing of a marshmallow than the ringing of a bell. The vibration damps itself out very quickly.

Hod has investigated how fast things can damp out. He find it is reciprocal to the TEMPERATURE. As the temp goes to zero the minimum possible relaxation time goes to infinity.

He says this is a practical explanation of the THIRD LAW because the colder it gets the longer it takes to settle down to the next lower temp. So Achilles never freezes the rabbit. Something like that.

===quote===
Summary.— In this Letter we have derived a universal
bound on relaxation times of perturbed thermodynamic
systems, $$\tau \geq \hbar/\pi T$$. The relaxation bound is a direct
consequence of quantum information theory and thermodynamic
considerations.
We conjecture that a relation of this form could serve
as a quantitative way to express the third-law of thermodynamics.
Namely, one cannot reach a temperature T
in a timescale shorter than $$\hbar/\pi T$$ (which indeed goes to
infinity in the limit of absolute zero of temperature, in
accord with the third-law).
Remarkably, black holes comply with the dynamical
bound; in fact they have relaxation times which are of
the same order of magnitude as $$\tau_{min}$$, the minimal relaxation
time allowed by quantum theory. Moreover, extremal
black holes (in the TBH ->0 limit) actually attain
the bound– their relaxation time is infinitely long. Since
black holes saturate the fundamental bound, we conclude
that when judged by their relaxation properties, black
holes are the most extreme objects in nature.
===endquote===
http://arxiv.org/abs/gr-qc/0611004
Universal Bound on Dynamical Relaxation Times and Black-Hole Quasinormal Ringing
Shahar Hod
4 pages

"From information theory and thermodynamic considerations a universal bound on the relaxation time $$\tau$$ of a perturbed system is inferred, $$\tau \geq \hbar/\pi T$$, where T is the system's temperature. We prove that black holes comply with the bound; in fact they actually saturate it. Thus, when judged by their relaxation properties, black holes are the most extreme objects in nature, having the maximum relaxation rate which is allowed by quantum theory. "

Last edited: Nov 2, 2006
2. Nov 2, 2006