Nuclear incompressibility at finite temperature and entropy

Features of the nuclear isothermal incompressibility κ and adiabatic incompressibility κQ are investigated. The calculations are done at zero and finite temperatures and non-zero entropy and for several equations of state with a long range attraction and a short range repulsion. It is shown that κQ decreases with increasing entropy while the isothermal κ increases with increasing T. A duality is found between the adiabatic κQ and the T=0 isothermal κ. The effect of correlations on κ is studied. A peak in κ can occur from attractive scattering correlations in various two-nucleon spin-isospin channels. The second virial coefficient or ρ2 term in P versus density parallels a result that appears in the theory of superconductivity.