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

[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 T_BH ->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. "

 

[selfAdjoint]

Hunh! Not only in QG! This result could have a big effect on condensed matter physics, which let us recall, is about 90% of all physics done, and has its own "Beyond the SM" sector, eg. nonlinear optics and fractional quantum Hall effect.

 

[Entropia]

This new result by Shahar Hod is truly remarkable and has important implications for our understanding of black holes and their behavior. By connecting the Third Law of Thermodynamics to the relaxation time of perturbed thermodynamic systems, Hod has provided a clear and elegant explanation for the behavior of black holes.

The fact that black holes comply with this universal bound and even saturate it, shows that they are the most extreme objects in nature when it comes to relaxation properties. This is a significant finding, as it further solidifies the connection between black holes and thermodynamics.

Hod's work also has the potential to impact our understanding of Quantum Gravity, as it provides a new perspective on the behavior of black holes and their role in the fundamental laws of physics.

Overall, this is a beautiful and important contribution to the field of black hole physics and I look forward to seeing further developments in this area from Shahar Hod.