I want to know how thermodynamic quantities T,P, H change if the system is moving with respect to the frame of reference of observation with velocity which is comparable to the velocity of light.
1) Most of the textbooks I use actually sidestep the problem, by analyzing the thermodynamics in the local rest frame of whatever fluid exists, so that they don't have to consider the issue at all.
2) Other approaches exist. I'm rather fond of http://arxiv.org/abs/physics/0505004 myself. The paper has a reference list of some other approaches, and mentions that the topic has a "long and controversial history". The particular approach used by this paper is based on an approach pioneeered by Van Kampen and Israel. One of the things I like about this paper is that it is very short.
3) Unfortunately I can't personally comment on the relative popularity of the approach in the paper I cite above vs other approaches to covariant formulations of thermodynamics (such as those mentioned in the reference list of this paper for instance). Nor can I say much about the "controversial history" of the topic - thermodynamics isn't one of my main interests. In the past, where this question has arisen before, we haven't had many comments from other posters on these topics either. I hope we can get Chris Hillman to say a few words about these issues.
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