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