Can we use thermodynamics in the systems with gravity?

Abstract

It is shown that the thermodynamical parameters (temperature, pressure, entropy) as well as the concept of “thermodynamical equilibrium”, in general, cannot be introduced for systems with long-range interactions (gravity). Exceptions are dense systems (stars, planets, gas clouds), where the local equilibrium is caused by short-range forces, as well as by the creation and annihilation of photons. Local equilibrium can also be justified for cosmic microwave background radiation. It is shown that, despite the fact that the radiation of a black hole approximately corresponds to the radiation of a black body, it is impossible to introduce entropy and temperature of a black hole. Restrictions for the application of the thermodynamic parameters to the evolution of the universe as a whole are considered.