Thermodynamics of pairing in mesoscopic systems

Using numerical and analytical methods implemented for different models we conduct a systematic study of thermodynamic properties of pairing correlation in mesoscopic nuclear systems. Various quantities are calculated and analyzed using the exact solution of pairing. An in-depth comparison of canonical, grand canonical, and microcanonical ensemble is conducted. The nature of the pairing phase transition in a small system is of a particular interest. We discuss the onset of discontinuity in the thermodynamic variables, fluctuations, and evolution of zeros of the canonical and grand canonical partition functions in the complex plane. The behavior of the Invariant Correlational Entropy is also studied in the transitional region of interest. The change in the character of the phase transition due to the presence of magnetic field is discussed along with studies of superconducting thermodynamics.