The definitions of thermodynamic equilibrium in general relativistic curved spacetime background are presented respectively by use of relativistic hydrodynamics, kinetic theory and stochastic thermodynamics. The connections and differences between these definitions are also discussed. In particular, the equilibrium states defined via first order hydrodynamics can be unstable, whereas those defined via kinetic theory are always stable.

Thermodynamic equilibrium is a fundamental concept in thermodynamics and statistical physics. There are different definitions for this concept in the literature which varies drastically. The aim of this work is to classify different definitions, compare their similarities and dissimilarities, clarify the range of their applicability, and finally suggest an alternative definition which is applicable for describing macroscopic evolution of thermodynamic systems.