Classical statistical thermodynamics is one of the oldest, most well-established physical theories and its basis and results have not been challenged within its domain since the time of Boltzmann. Special relativity, however, introduces some constraints as well as ambiguities into such a theory. For example, the cornerstone of classical statistical mechanics, the Maxwell-Boltzmann (MB) distribution does not respect the maximal velocity of light, the cornerstone of special relativity. Additionally, the Lorentz transformation of temperature, i.e. how a moving body's temperature compares to its rest frame value, has long caused controversies. Special relativity also introduces a new concept of proper time, which could potentially affect fundamental concepts of ergodicity and time-averaging in thermodynamics.
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