Despite their importance for solar thermal power applications, phase-diagrams of molten salt mixture heat transfer fluids (HTFs) are not readily accessible from first principles. We present a molecular dynamics scheme general enough to identify eutectics of any HTF candidate mixture. The eutectic mixture and temperature are located using the liquid mixture free energy and the pure component solid-liquid free energy differences. The liquid mixture free energy is obtained using thermodynamic integration over particle identity transmutations sampled with molecular dynamics at a single temperature. According to Carnot's cycle, the maximum efficiency of solar thermal power facilities increases with the temperature difference between melting and thermal decomposition of employed heat transfer fluids (HTFs). Consequently, new formulations of low melting but temperature resistant molten salt mixtures are actively sought [1]. Competitive formulations currently include eutectics of alkali and alkali-metal earth nitrates and nitrite mixtures. Unfortunately, the dimensionality of the combinatorial multicomponent space of all possible cations and anions prohibits exhaustive scanning using computer simulation. Once an optimal HTF formulation is identified, however, its realization through simple mixing is readily accomplished in experiment. Identifying new HTFs therefore represents a rewarding challenge for atomistic first principles materials design efforts using theory and computation. Ab initio (AI) based design, through an efficient combination of first principles methods and optimization algorithms [2], has already been applied to inverting band structures [3], identifying stable alloys [4], designing heterogeneous catalysts [5,6], or discovering ternary metal oxides for batteries [7]. Identity transformations, also called "alchemical" transmutations [8], have been successfully applied to compute compositions in the earth's core [9], phase stability in solid solutions [10], and a wide variety of biochemical applications [11], among others.The Gibbs criteria for phase equilibrium dictates that temperature, pressure, and chemical potential of individual components must be equal in coexisting phases. Therefore, knowledge not only of average liquid configurations but also of the solid mixture's structure is essential. For phase transitions of mixtures, the problem is hence strongly linked to the challenge of predicting molecular crystals from first principles [12], which has been addressed for co-crystals only recently [7,13] in mapping out entire phase diagrams. For the identification of HTF mixtures with minimal melting points, however, it is sufficient to simply focus on eutectics, rather than having to screen the entire solid-liquid phase diagram. Here, we present a first principles approach for directly estimating eutectic compositions and temperatures for any number of components, relying on a combination of only a couple of molecular dynamics (MD) calculations per mole fraction at a single temperature and knowledge ab...