I A possible solution to the cosmic lithium problem

[Chronos]

This paper; https://arxiv.org/abs/1701.04149, Non-extensive Statistics Solution to the Cosmological Lithium Problem, offers a plausible solution to the cosmic lithium problem that has baffled astrophysics, and BBN aficionados, for decades. Unlike prior efforts, it does not invoke any BTSM particles or new physics, just a twist on statistical modeling which looks entirely reasonable. Past efforts have failed largely because you cannot get an acceptable range for lithium abundance without fouling up production of other light elements during BBN. I am curious if this approach [Tsallis statistics] has been used before in astrophysical applications. All I could turn up was some fairly obscure papers on DM distribution and interstellar turbulence.

 

[phyzguy]

Wow. Thanks for pointing this out. I find it very plausible. It is easy for me to believe that the velocity distribution in the early expanding universe might not match Maxwell-Boltzmann statistics exactly. Note that in addition to solving the lithium problem, it also improves the agreement between the model and the data for deuterium.

 

[Chalnoth]

This paper; https://arxiv.org/abs/1701.04149, Non-extensive Statistics Solution to the Cosmological Lithium Problem, offers a plausible solution to the cosmic lithium problem that has baffled astrophysics, and BBN aficionados, for decades. Unlike prior efforts, it does not invoke any BTSM particles or new physics, just a twist on statistical modeling which looks entirely reasonable. Past efforts have failed largely because you cannot get an acceptable range for lithium abundance without fouling up production of other light elements during BBN. I am curious if this approach [Tsallis statistics] has been used before in astrophysical applications. All I could turn up was some fairly obscure papers on DM distribution and interstellar turbulence.

Huh. Interesting. I'll be curious to see if there are some good further investigations into this. On the one hand, it'd be disappointing because if this is true because it removes a possible experimental test for new physics. On the other, it'd be yet another piece of supporting evidence for the standard model of cosmology.

 

[Chronos]

I hear you. There are plenty of reasons to hope for new physics, but the encouragement seems to keep melting. I'm pretty happy with the standard model. It still looks very robust. That is not surprising given collective intellectual inertia usually defeats heroic new ideas. I do, however, secretly hope it will be blown up some day - in a manner akin to the way GR blew up classical physics paradigms. I'm an old guy who needs a compelling reason to forsake chopping firewood - its hard work, but, keeps you warm at night.

 

[DrClaude]

I don't want to go down the Tsallis rabbit hole, but would like to point out the following articles:
Critique of q-entropy for thermal statistics
Comment on “Critique of q-entropy for thermal statistics”
Reply to “Comment on ‘Critique of q-entropy for thermal statistics’ ”

 

[Chronos]

Thanks Claude, that's what I was really curious about. I appreciate Nauenberg's critique, even if I don't entirely understand it. I can't help but wonder if you can't just relax the objectionable assumptions/definitions enough to accommodate Tsallis, instead of tossing out the baby

 

[Chalnoth]

I don't want to go down the Tsallis rabbit hole, but would like to point out the following articles:
Critique of q-entropy for thermal statistics
Comment on “Critique of q-entropy for thermal statistics”
Reply to “Comment on ‘Critique of q-entropy for thermal statistics’ ”

Curious. I wonder how salient this critique is.

My general expectation is that when you start describing systems as being out-of-equilibrium, then a number of thermodynamic properties are expected to no longer apply exactly. So my question would then be: does it matter? Is the math still a decent approximation to the physical behavior of an out-of-equilibrium system? Or do the shortcomings actually prevent this from being relevant?

I guess what I'd need to be convinced one way or the other would be to see an experiment with a physical system that is prepared in a specific out-of-equilibrium state which should be relevant to Tsallis statistics, and ask if the properties of said system follow the behavior laid out by Tsallis statistics.

 

[DrClaude]

The problem with the Tsallis q-entropy appears when the parameter q is used as a fitting parameter. This gives too much flexibility to the Tsallis function, since it can encompass many functional forms, including a Gaussian and a Lorentzian. Basically, you can fit an elephant with it!

So unless there is a physical basis for a particular choice of q, this is just hunting for whatever fits. I must admit that I did not read the paper, only the abstract, but it sounds like q-fitting.

 

[Chronos]

A reasonably 'unbiased' review of the pros and cons of q-fitting is offered here; http://portal.cbpf.br/attachments/f0d1f61c35a13f8821193b0dd0d51456b14a93ca.pdf. I can live with curve fitting to the extent it yields reproducible, predictive results. That strikes me as a valid scientific practice. It admittedly feels a bit ironic to apply the qualifier 'unbiased' to a paper addressing statistical bias.

 

[Chalnoth]

The problem with the Tsallis q-entropy appears when the parameter q is used as a fitting parameter. This gives too much flexibility to the Tsallis function, since it can encompass many functional forms, including a Gaussian and a Lorentzian. Basically, you can fit an elephant with it!

That's a good point, though I wouldn't go so far as that. Presumably it can encompass many functional forms, but a single parameter isn't going to provide that much flexibility. However, the criticism is solid because adding an additional fit parameter will always improve the fit, regardless of whether or not the parameter is justified. When doing such fitting, at a bare minimum it's important to show that there is sufficient improvement to the fit that something real is probably being captured.

So unless there is a physical basis for a particular choice of q, this is just hunting for whatever fits. I must admit that I did not read the paper, only the abstract, but it sounds like q-fitting.

Yes, it's q-fitting. They could probably fix this shortcoming with some simulations that demonstrate that it's warranted. Assuming the calculations are tractable, our understanding of nuclear physics should be more than adequate to determine whether or not Tsallis statistics with q in the range used by this paper is justified.

 

[Chronos]

q-fitting is already widely used by CERN.

 

[Dr. Courtney]

The problem with the Tsallis q-entropy appears when the parameter q is used as a fitting parameter. This gives too much flexibility to the Tsallis function, since it can encompass many functional forms, including a Gaussian and a Lorentzian. Basically, you can fit an elephant with it!

So unless there is a physical basis for a particular choice of q, this is just hunting for whatever fits. I must admit that I did not read the paper, only the abstract, but it sounds like q-fitting.

Sounds like a fudge factor. Not a show stopper, but models are more compelling if a case is made BEFOREHAND what the value of the fitting parameter should be.

 

[e.bar.goum]

Thank you for alerting me to this rather interesting paper. However, before I'm going to get too excited, I would like to see some work in a mechanism for this deviation from M-B during BBN, as well as a prediction for the value of q. In general, I find that just adding another parameter to your model and fitting, then declaring that you've fixed a problem is a not very useful way to do physics.

Certainly something to keep an eye on, anyway.

 

[mfb]

They introduce one new parameter and fit it to data to make one observed value agree better? I am not impressed. The D/H ratio is fine without that new parameter.
The idea of deviations from a Maxwell-Boltzmann distribution is nice, but I would expect a discussion which type of deviation to expect without a fit to data.

Looking at figure 2, the distribution looks very odd. Which physical process should lead to such a sharp cutoff at a given energy?

q-fitting is already widely used by CERN.

What do you mean?

 

[Dr. Courtney]

Thank you for alerting me to this rather interesting paper. However, before I'm going to get too excited, I would like to see some work in a mechanism for this deviation from M-B during BBN, as well as a prediction for the value of q. In general, I find that just adding another parameter to your model and fitting, then declaring that you've fixed a problem is a not very useful way to do physics.

Certainly something to keep an eye on, anyway.

For me, the fact that the equilibrium assumption of M-B is not satisfied seems to justify A deviation from M-B distribution.

The part that needs to be motivated is why _THIS_ specific deviation from M-B with _THIS_ specific value of q.

However, this development is worthy of publication and consideration, because it allows a much broader pool of physicists to work on the above issues.

 

[Chronos]

I did some brushing up on Dr. Tsallis and he certainly is an interesting story. I would stop short of characterizing him as the Einstein of Boltzmann's statistics. He does come off as a bit flaky, but, some of the best biscuits share this trait.