  In this paper, we investigate the thermodynamic behavior of a rotating
Bose-Einstein condensation with non-zero interatomic interactions
theoretically. The analysis relies on a semiclassical Hartree-Fock
approximation where an integral is performed over the phase space and function
of the grand canonical ensemble is derived. Subsequently, we use this result to
derive several thermodynamic quantities including the condensate fraction,
critical temperature, entropy and heat capacity. Thereby, we investigate the
effect of the rotation rate and interactions parameter on the thermodynamic
behavior. The role of finite size is discussed. Our approach can be extended to
consider the rotating condensate in optical potential.
