Local Thermodynamic Equilibrium at Three Levels

We present coordinated formulations of local thermodynamical equilibrium conditions at three levels, namely the macroscopic one of classical thermodynamics, the mesoscopic one of hydrodynamical fluctuations and the microscopic one of quantum statistical mechanics. These conditions are all expressed in terms of the hydrodynamical variables of the macroscopic picture, and the quantum statistical ones are shown to imply a local version of the zeroth law.