Thermodynamic equilibrium and relativity: killing vectors and lie derivatives

Abstract

The main concepts of general relativistic thermodynamics and general relativistic statistical mechanics are reviewed in a quantum framework. The main building block of the proper relativistic extension of classical thermodynamics laws is the four-temperature vector β. The general relativistic thermodynamic equilibrium condition demands β to be a Killing vector field. A remarkable consequence of this condition is that all Lie derivatives of all physical observables along the four-temperature flow vanish.