Relativistic thermodynamics problem

[bernhard.rothenstein]

Authors (Tolmann, Arzelies) consider that proper temperature T(0) and non-proper one T are related in the I inertial reference frame by
T=T(0)/(1-uu/cc)^1/2 (1) whereas in I' they are related by T'=T(0)/(1-u'u'/cc)^1/2 (2). Expressing the right side of (1) as a function of u' via the addition law of relativistic velocities we obtain
T=T'(1+Vu'/cc)/(1-VxV/cc)^1/2. (3)
Do you see some physics behind (3). Has u'T'/cc a physical meaning eventually via the Boltzmann constant?
Thanks

 

[pervect]

The question of how to treat relativistic thermodynamics comes up from time to time, but usually doesn't get much of an answer. My thinking on the topic is based on the arguments presented in http://arxiv.org/abs/physics/0505004

which argues for inverse temperature as a 4-vector and which I personally find convincing. Unfortunately, I have *not* read all the relevant literature in this field (relativistic thermodynamics) thus it's quite possible that as a result of this I'm missing some of the fine or not-so-fine points.

Here are a couple of quotes from the above paper:

Let us generalize the above statement to relativity. Heat is a form of energy in non-relativistic thermodynamics, where the energy and momentum
are distinct quantities. In relativity, however, the energy and momentum are
components of one physical entity, energy-momentum four vector namely, and thus cannot be treated independently. Therefore we must treat the energy-momentum exchange between the objects, not energy alone.

Consequently, the inverse temperature must have four components, , corresponding to each component of energy-momentum four vector.

Apparently there has been some amount of controversy in the field, the authors state:

Theory of relativistic thermodynamics has a long and controversial history
(see, e.g., [1] and references therein). The controversy seems to have been
settled more or less by the end of 1960s [2], however, papers are still being
published to this date (e.g., [3]).

Thus the early papers such as those of Tollman may not be representative of the current thinking.

Unfortunately, it is not particularly clear to me how one could go about demonstrating whether or not the above paper is representative of current thinking either - all I can say is that I find the arguments presented in this paper convincing.