kinetic symmetry energy originates from the Fermi-Dirac distribution [@thesis].

Finally, we get a density and isospin-single particle potential in nuclear matter as follows: $$\begin{aligned}
V_{\tau}(\rho,\delta)&=& \alpha\left(\frac{\rho}{\rho_0}\right)+
\beta\left(\frac{\rho}{\rho_0}\right)^{\gamma}+
E^{pot}_{Sym}(\rho)\delta^2 \nonumber\\
& &+\frac{\partial E^{pot}_{Sym}(\rho)}{\partial\rho}\rho\delta^2+
E^{pot}_{Sym}(\rho)\rho\frac{\partial\delta^2}
{\partial\rho_{\tau,\tau^\prime}}.\end{aligned}$$ Here $\tau \neq \tau^\prime$, $\frac{\partial\delta^2}{\partial\rho_n}~=~
\frac{4 \delta \rho_p}{\rho^2}$, and $\frac{\partial\delta^2}
{\partial\rho_p}~=~\frac{-4 \delta \rho_n}{\rho^2}$. The potential also depends on the momentum-dependent interactions, which are optional in the IQMD model.

Note that the $\gamma$ used in the determination of the equation of state and $\gamma_i$ used in the determination of symmetry energy are different parameters. The interesting feature of symmetry energy is that its value increases with decreasing $\gamma_i$ at sub-saturation densities, while the opposite is true at supra-saturation densities. In other words, soft symmetry energy is more pronounced at sub-saturation densities, while stiff symmetry energy is more pronounced at supra-saturation densities.

In the calculations, we use the isospin-dependent in-medium cross section in the collision term and the Pauli blocking effects as in the QMD model [@Aich91]. The cluster yields are calculated by means of the coalescence model, in which particles with relative momentum smaller than $P_{Fermi}$ and relative distance smaller than $R_{0}$ are coalesced into a one cluster. The value of $R_{0}$ and $P_{Fermi}$ for the present 