Gravity and Thermodynamics in globular clusters. Theoretical developments and results by numerical simulations

We develop models of globular clusters (GCs) with a different approach by applying thermodynamic principles to a Boltzmann distribution function, with an Hamiltonian function which contains an effective potential depending on the kinetic energy of the stars, due to the effect of tidal interactions induced by the hosting galaxy. The Hamiltonian function is solution of the Fokker-Planck equation solved in a different way with respect to the King approach. Interesting results implying a different critical point for the onset of gravothermal catastrophe are presented, as well numerical simulations conrming the presence and the predicted form of the effective potential.