# Relativistic thermodynamics controversy?

## Main Question or Discussion Point

The following papers on relativistic thermodynamics appear to disagree with each other.

Which expert has the correct interpretation of relativistics thermodynamics?

P' and T' are the transformed pressure and temperature and y is the usual gamma factor of special relativity.

P' = Py^2 , T' = Ty http://arxiv.org/PS_cache/arxiv/pdf/...712.3793v2.pdf [Broken]

P' = ? , T' = ? http://arxiv.org/PS_cache/physics/pd.../0303091v3.pdf [Broken]

P' = ? , T' = ? http://arxiv.org/PS_cache/gr-qc/pdf/9803/9803007v2.pdf

P' = P , T' = Ty http://arxiv.org/PS_cache/arxiv/pdf/...801.2639v1.pdf [Broken]

P' = P , T= T/y http://arxiv.org/PS_cache/physics/pd.../0505004v2.pdf [Broken]

P' = P, T= T/y is my interpretation of the last paper which is Pervect's favourite paper on the subject. Unfortunately it fails to explicity come to a conclusion and leaves that to the imagination of the reader. Their approach is interesting and looks promising. The final sentence of the paper is "Now we have the clearly covariant definition of the entropy, other thermodynamical quantities can be derived covariantly using it."

The question is, is there anyone on this forum with ability to fill in the gaps and implicity specify the "other thermodynamic quantities"?

They refer to a 4 volume and a 4 inverse temperature. Presumably this will result in an invariant quantity S something like:

$$s = \sqrt{\left(\frac{1}{(nkT)^2} - \frac{1}{(PV_x)^2} - \frac{1}{(PV_y)^2} -\frac{1}{(PV_z)^2\right)} = constant?$$

and presumably there is a temperature-volume tensor that a standard Lorentz boost can be performed on.

The final equation in that paper is:

$$d(S) = \frac{V_0 d(e)}{k_BT} - \frac{Pd(V_0)}{k_BT}$$

where e is the (proper) energy density measured in the co-moving frame and k_B is Boltzman's constant.

Given that the energy density e is invariant and assuming that pressure P is invariant, then T' transforms as T/y if we assume volume V and d(V) also transform as V' = V/y.

Tolman's book on relativity and thermodynamics also concludes P' = P, T= T/y but the book is rather old and uses a different method to came to that conclusion. The conclusion that T' transforms as T/y is also at odds with the Planck Einstein temperature that transforms as T' = T*y.

Are the members of this forum able to settle the controversy by coming up with a clear and unambiguous definition of how temperature, pressure and volume transform with relative motion?

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Hmmm. My first instinct is that equilibrium might be a tricky concept to apply in a fully covariant fashion. What is in statistical equilibrium in one frame might not be in another...

By the way, none of the links work --- please link to the abstract page rather than to the PDFs --- arxiv generates the pdfs on the fly when requested.

By the way, none of the links work --- please link to the abstract page rather than to the PDFs --- arxiv generates the pdfs on the fly when requested.
Sorry, I think I have fixed the problem in the links listed below. If that fails, I will have to track down the original ARXIV abstract pages when I have more time.

P' = Py^2 , T' = Ty http://arxiv.org/PS_cache/arxiv/pdf/0712/0712.3793v2.pdf" [Broken]

P' = ? , T' = ? http://arxiv.org/PS_cache/physics/pdf/0303/0303091v3.pdf" [Broken]

P' = ? , T' = ? http://arxiv.org/PS_cache/gr-qc/pdf/9803/9803007v2.pdf" [Broken]

P' = P , T' = Ty http://arxiv.org/PS_cache/arxiv/pdf/0801/0801.2639v1.pdf" [Broken]

P' = P , T= T/y http://arxiv.org/PS_cache/physics/pdf/0505/0505004v2.pdf" [Broken]

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Sorry, I think I have fixed the problem in the links listed below. If that fails, I will have to track down the original ARXIV abstract pages when I have more time.
Actually, please do track down the abstract pages. Even better would be to be able to say whether any of these papers actually passed peer-review in a reputable journal. I'm afraid that arxiv contains far too much questionable material for it to be taken at face-value. Having a quick glance at the papers, they all seem to simply assume that equilibrium is possible in more than one frame --- something I have deep misgivings about.

I have had my knuckles smacked for linking to papers that are not peer reviewed. To be honest I have not been able to find any peer reviewed papars on the subject of relativistic thermodynamics and would be happy if anyone here could link to one so we can discuss it.

Of the papers in the list, the last paper was cited by Pervect in this post: https://www.physicsforums.com/showpost.php?p=1483418&postcount=3 and the first was cited by AstoRoyale in this post here: https://www.physicsforums.com/showpost.php?p=1617003&postcount=59

I respectfully ask the forum moderators if we can discuss those two papers (not peer reviewed) on the grounds that they are already cited by other PF members in other PF threads?

I also have access to book on relativistic thermodynamice by Tolman. Is Tolman reguarded as a respectable mainstream author and are we allowed to discuss his book?

Finally, can any senior PF member state what the current accepted mainstream view on relativistic thermodymanics is and point to some peer reviewed papers or text books that can be referred to? The policy of PF is to guide its readers to the mainstream view and I am only asking for that guidance.

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The references of those papers cite various things by Einstein, Ott and Landsberg, who respectively think that moving objects are colder, hotter and invariant. You can try reading those and seeing what they do, how they differ in their assumptions and why they disagree with each other. However, given the fact that there does seem to exist genuine disagreement, I would suspect that the matter has not been settled. Also since neither SR nor thermodynamics are complicated in their mathematical settings, the problem is likely to be that of a foundational nature --- i.e. what does temperature mean for a moving object.

My colleagues and I discussed this over a few lunches, and decided that at least for an ideal gas, moving should make it hotter --- in the sense that if you held a thermometer in the moving gas it would register a higher reading than a thermometer that was co-moving with the gas. However, it wasn't clear from our napkin jottings how exactly the temperature would transform. Another case is that of a photon gas, in which case you would observe a transform congruent with Doppler shifting; it is not clear however if this is going to give the same answer as for the ideal gas.

xantox
Gold Member
This subject has been furiously controversial for a long time. Since the probability distribution in the relativistic regime is no longer Maxwell-Boltzmann, temperature may be defined in various ways, so that for each definition you will obtain one of those transformations, generating confusions which may remind those related to the multiple definitions of mass in special relativity.

The present view is that this whole questioning about how classical thermodynamic variables transform under the Lorentz group is fundamentally inappropriate, since the theory of thermodynamics itself has to be reformulated in a relativistic framework.

The first such approach was due to Israel-Stewart, and in their covariant formalism the above question has no longer any meaning, since eg temperature becomes a 4-vector with a different definition than in classical thermodynamics and which is not homogeneous even in thermal equilibrium.

Moreover, in a quantum analysis it was suggested that the transformations such as T'(T,v) =γαT where α=-1 (Planck-Einstein), +1 (Ott) or 0 (Landsberg) do not conserve a Planckian spectrum and so do not exist in the general case.

Essential bibliography:

C. Liu, "Einstein and relativistic thermodynamics in 1952: a historical and critical study of a strange episode in the history of modern physics". The British Journal for the HIstory of Science 25, 185-206 (1992) et "Is There a Relativistic Thermodynamics? A Case Study of the Meaning of Special Relativity", Studies in the History and Philosophy of Modern Physics, 25, 983-1004 (1994).

A. Einstein, "Über das Relativitäts Prinzip und die aus demselben gezogenen Folgerungen", Jahrb. Radioaktiv. Elektron., 4 (1907).

M. Planck, Ann. Phys. Leipzig, 26, 1 (1908).

F. Jüttner, "Das Maxwellsche Gesetz der Geschwindigkeitsverteilung in der Relativtheorie", Ann. Physik und Chemie 34, 856-882 (1911).

H. Ott, "Lorentz transformation der Warme und der Temperatur", Z. Phys., 175:1, 70 (1963).

M. Landsberg, "Does a Moving Body appear Cool?", Nature 212, 571-572 (1966) et Nature 214, 903-904 (1967).

R. Aldrovandi, J. Gariel, "On the riddle of the moving thermometers", Physics Letter A, 170:1, 5-10 (1992).

C. Fenech, J. P. Vigier, "Variation of local heat energy and local temperatures under Lorentz transformations", Physics Letters A, 215, 247-253 (1996).

R. C. Tolman, "Relativity, Thermodynamics and Cosmology", Dover (1934); N. ed. (1987).

W. Israel, J. M. Stewart, "Transient relativistic thermodynamics and kinetic theory", Annals of Physics, 118:2, 341-372 (1979), cfr also W. Israel, "Relativistic thermodynamics, thermofield statistics and superfluids", Journal of non-equilibrium thermodynamics, 11:3-4, 295-316 (1986).

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pervect
Staff Emeritus
I have had my knuckles smacked for linking to papers that are not peer reviewed.
Note that my favorite paper does have a peer-reviewed version. See for instance Physics Letters A, specifically:

http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6TVM-4HR7448-2&_user=10&_rdoc=1&_fmt=&_orig=search&_sort=d&view=c&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=2c4f0f4d390c7e926113017a5d655231

and compare the abstract and author with the arxiv version:

http://arxiv.org/abs/physics/0505004

(Note that it's better to link to the abstract as above for arxiv papers).

It is generally possible and worthwhile to do a quick search to see if a particular arxiv paper has been published or not as a rough guide to its merits.

I can't guarantee that there won't be minor differences between the arxiv version and the Physics Letters A version. Nor can I personally guarantee how representative of "mainstream" views this paper is. What i can say is that it's fairly short, not too hard to understand, and seems to be sensible with a good bibliography. I'd be interested in xantox's comments on this paper, by treating inverse temperature as a 4-vector it seems to be a variant on the Israel-Stewart approach xantox mentions - a modifcation due to Van Kampen.

xantox
Gold Member
I'd be interested in xantox's comments on this paper, by treating inverse temperature as a 4-vector it seems to be a variant on the Israel-Stewart approach xantox mentions - a modifcation due to Van Kampen.
Van Kampen theory was indeed an early proposal (together with Landsberg's) of the fully covariant theory further developed in the eighties by Israel and Stewart.

In this theory, when translating the fundamental thermodynamics relation in the Euler form from classical to relativistic, the 1/T term becomes an observer-dependent 4-vector.

Both this and a microscopic (quantum) analysis suggest that the mentioned transformations simply do not exist, and that a scalar (proper) invariant definition of temperature should be preferred, just like one would prefer to use proper mass as a definition of mass.

The Nakamura paper follows the above authors and is focusing in the technicalities of the definition of the primary variables used to characterize the equilibrium states of the system.

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Relativistic Thermodynamics

Geez..........
Just as in the standard model G is insignificant. I would think that to try to discern cosmologically relativistic thermodynamics should show minimal anistrophies i.e. CMB.

To Pervect or Genneth:

With reference to the paper that pervect calls his favorite, it ends with the enticing statement "Now we have the clearly covariant definition of the entropy, other thermodynamical quantities can be derived covariantly using it." which seems to imply that the other thermodynamical quantities can be derived so easily by anyone with a reasonable grasp of thermodymics and relativity that there was no need for the authors to explicity state them. Would it possible for someone to explicity state them here?

Also, I assume that their use of the term "covariant" is what most people mean by invariant under Lorentz transformation. Would that be correct?

Could Pervect give a definition of "four volume" in accessible terms and an expression for the four inverse temperature as mentioned in the paper in the form of a four vector equation or matrix so that we might understand the paper better?