Relativistic temperature

A measurement theory for the temperature of relativistic systems is developed. The resulting operational approach is shown to be quasi-local and therefore may be applicable in general Riemannian manifolds even when there are temperature gradients which induce heat flows. The surprising feature of our analysis is that it leads to a bifurcation of the temperature concept into two distinctly different measurable quantities: one a frame invariant scalar field which a local co-moving observer would tend to identify with the local temperature and employ in the definition of entropy, the other a frame dependent, but nevertheless locally determinable quantity which governs the flow of heat and the ability to extract work. The two quantities differ by the bookkeeping methodology employed to calibrate the thermometer. A simple relationship between the two temperatures can be established if a preferred Killing vector field is available in the Riemannian manifold