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## 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

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:

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

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

The final equation in that paper is:

[tex] d(S) = \frac{V_0 d(e)}{k_BT} - \frac{Pd(V_0)}{k_BT} [/tex]

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?

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:

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

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

The final equation in that paper is:

[tex] d(S) = \frac{V_0 d(e)}{k_BT} - \frac{Pd(V_0)}{k_BT} [/tex]

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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