We systematically investigate the thermodynamic properties of homogeneous nuclear matter with light clusters at low densities and finite temperatures using a generalized nonlinear relativistic mean-field ( gNL-RMF ) model , in which light clusters up to \alpha ( 1 \leq A \leq 4 ) are included as explicit degrees of freedom and treated as point-like particles with their interactions described by meson exchanges and the medium effects on the cluster binding energies are described by density- and temperature-dependent energy shifts with the parameters obtained by fitting the experimental cluster Mott densities .
We find that the composition of low density nuclear matter with light clusters is essentially determined by the density- and temperature-dependence of the cluster binding energy shifts .
Compared with the values of the conventional ( second-order ) symmetry energy , symmetry free energy and symmetry entropy , their fourth-order values are found to be significant at low densities ( n \sim 10 ^ { -3 } fm ^ { -3 } ) and low temperatures ( T \lesssim 3 MeV ) , indicating the invalidity of the empirical parabolic law for the isospin asymmetry dependence of these nuclear matter properties .
Our results indicate that in the density region of n \gtrsim 0.02 fm ^ { -3 } , the clustering effects become insignificant and the nuclear matter is dominated by nucleon degree of freedom .
In addition , we compare the gNL-RMF model predictions with the corresponding experimental data on the symmetry energy and symmetry free energy at low densities and finite temperatures extracted from heavy-ion collisions , and reasonable agreement is found .