Thermodynamics of Fluid Elements in the Context of Turbulent Isothermal Self-Gravitating Molecular Clouds

In the present work we suggest a new approach for studying the equilibrium states of an hydrodynamic isothermal turbulent self-gravitating system, as statistical model for a molecular cloud. The main hypothesis is that the local turbulent motion of fluid elements is purely chaotic and can be regarded as a perfect gas. Then the turbulent kinetic energy, per one fluid element, can be substituted for the temperature of chaotic motion of the fluid elements. Using this we write down effective formulae for internal and total energy and the first principal of thermodynamics. Then we obtain expressions for entropy, free energy, and Gibbs potential. Searching for equilibrium states we explore two possible systems: the canonical ensemble and the grand canonical ensemble. Studying the former we conclude that there is no extremum for the free energy. In the latter system we obtain a minimum for the Gibbs potential when macro-temperature and pressure of the cloud are equal to those of the surrounding medium. This minimum corresponds to a possible stable local equilibrium state of our system.