Nuclear incompressibility in asymmetric systems at finite temperature and entropy

The nuclear incompressibility κ is investigated in asymmetric systems in a mean field model. The calculations are done at zero and finite temperatures and include surface, Coulomb and symmetry energy terms for several equations of state. Also considered is the behavior of the incompressibility at constant entropy ${\kappa }_Q$ which is shown to have a very different behavior than the isothermal κ. Namely, ${\kappa }_Q$ decreases with increasing entropy while the isothermal κ increases with increasing T. A duality is found between the adiabatic ${\kappa }_Q$ and the $T=0$ isothermal κ. Analytic and also simple approximate expressions for κ are given which illustrate the role of various terms that enter into κ. Namely, properties of the interaction used, the value of the effective mass, and its density dependence all play an important role.