  The presented paper is an attempt to investigate the dynamical states of an
hydrodynamical isothermal turbulent self-gravitating system using some powerful
tools of the classical thermodynamics. Our main assumption, inspired by the
work of Keto et al. (2020), is that turbulent kinetic energy can be substituted
for the macro-temperature of chaotic motion of fluid elements. As a proper
sample for our system we use a model of turbulent self-gravitating isothermal
molecular cloud which is at final stages of its life-cycle, when the dynamics
is nearly in steady state. Starting from this point, we write down the internal
energy for a physically small cloud's volume, and then using the first
principle of thermodynamics obtain in explicit form the entropy, free energy,
and Gibbs potential for this volume. Setting fiducial boundary conditions for
the latter system (small volume) we explore its stability as a grand canonical
ensemble. Searching for extrema of the Gibbs potential we obtain conditions for
its minimum, which corresponds to a stable dynamical state of hydrodynamical
system. This result demonstrates the ability of our novel approach.
