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The main concepts of general relativistic thermodynamics and generalrelativistic statistical mechanics are reviewed. The main building block of theproper relativistic extension of the classical thermodynamics laws is thefour-temperature vector \beta, which plays a major role in the quantumframework and defines a very convenient hydrodynamic frame. The generalrelativistic thermodynamic equilibrium condition demands \beta to be a Killingvector field. We show that a remarkable consequence is that all Lie derivativesof all physical observables along the four-temperature flow must then vanish.

Thermodynamic equilibrium in relativity: four-temperature, Killing vectors and Lie derivatives