Different models are used to describe and parameterize enthalpy and free energy in GeSnSi alloys over the entire composition range from density-functional theory calculations and are used to explore if concentrated alloys in the equiatomic concentration range are thermodynamically feasible. It is found that the energetics are very well behaved and follow the expressions of a ternary regular solution rather closely. While a small asymmetry is found in the ideal solution energetics for the three binaries, it is found that the assumption of a symmetric ideal solution as underlying the quasichemical model does not change the general findings. All free energy contributions within this work are parameterized in different approximations, providing a complete parameter set that can be used for further thermodynamic studies of the GeSnSi alloy system. In the obtained results, the enthalpy of mixing of the SiSn system has rather large values, which is maintained more or less unchanged in the ternary system, making a concentrated ternary alloy thermodynamically unfavorable. Calculating the full free energy from adding configurational and vibrational entropy contributions does not change the overall situation.