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We study the equation of state at finite temperature and density intwo-flavor QCD with the RG-improved gluon action and the clover-improved Wilsonquark action on a $ 16^3 \times 4$ lattice. Along the lines of constant physicsat $m_{\rm PS}/m_{\rm V} = 0.65$ and 0.80, we compute the second and forthderivatives of the grand canonical partition function with respect to the quarkchemical potential $\mu_q = (\mu_u+\mu_d)/2$ and the isospin chemical potential$\mu_I = (\mu_u-\mu_d)/2$ at vanishing chemical potentials, and study thebehaviors of thermodynamic quantities at finite $\mu_q$ using these derivativesfor the case $\mu_I=0$. In particular, we study density fluctuations atnone-zero temperature and density by calculating the quark number and isospinsusceptibilities and their derivatives with respect to $\mu_q$. To suppressstatistical fluctuations, we also examine new techniques applicable at lowdensities. We find a large enhancement in the fluctuation of quark number whenthe density increased near the pseudo-critical temperature, suggesting acritical point at finite $\mu_q$ terminating the first order transition linebetween hadronic and quark gluon plasma phases. This result agrees with theprevious results using staggered-type quark actions qualitatively. Furthermore,we study heavy-quark free energies and Debye screening masses at finite densityby measuring the first and second derivatives of these quantities for variouscolor channels of heavy quark-quark and quark-anti-quark pairs. The resultssuggest that, to the leading order of $\mu_q$, the interaction between twoquarks becomes stronger at finite densities, while that between quark andanti-quark becomes weaker.

Equation of State and Heavy-Quark Free Energy at Finite Temperature and Density in Two Flavor Lattice QCD with Wilson Quark Action