Reversible martensitic transformations (MTs) are the origin of many fascinating phenomena, including the famous shape memory effect. In this work, we present a fully ab initio procedure to characterize MTs in alloys and to assess their reversibility. Specifically, we employ ab initio molecular dynamics data to parametrize a Landau expansion for the free energy of the MT. This analytical expansion makes it possible to determine the stability of the high-and low-temperature phases, to obtain the Ehrenfest order of the MT, and to quantify its free energy barrier and latent heat. We apply our model to the high-temperature shape memory alloy Ti-Ta, for which we observe remarkably small values for the metastability region (the interval of temperatures in which the highand low-temperature phases are metastable) and for the barrier: these small values are necessary conditions for the reversibility of MTs and distinguish shape memory alloys from other materials.A martensitic transformation (MT) [1] is a diffusionless phase transition, triggered by temperature or stress, that changes the symmetry of a high-temperature phase (austenite) and forms variants of a low temperature phase (martensite). Most of the MTs are irreversible, as dislocations, shear, and plastic deformation accumulate during the transformation. However, if the symmetry of martensite is lower than that of austenite and if the variations in lattice parameters and atomic volumes are small, the MT can be reverted, that is, the system can be switched between the two phases with small latent heat [2][3][4][5]. Reversible MTs in metals or polymers are appealing as they often result in the shape memory effect, the ability to recover a predetermined shape upon heating, and pseudoelasticity, the capacity to accommodate large deformations without plasticity [6][7][8]. Other examples in which reversible MTs are important include the recently discovered gum metals [9], where metastable phases have been observed to form via reversible transformations [10].An urgent technological challenge for actuator and biomedical applications is to identify alloys that exhibit reversible MTs that are stable during operational cycles. With very few exceptions [11], first principles investigations aiming to clarify the mechanisms underlying a MT generally rely on static, T = 0 K calculations. These, however, are often inadequate to describe the atomistic processes responsible for the dynamic and/or thermodynamic stabilization of the austenite phase at finite temperatures, as well as the interval of temperatures in which austenite and martensite are metastable (metastability region), the free energy barrier, the latent heat, and even the Ehrenfest order of a MT.To overcome these limitations we have employed ab initio molecular dynamics (aiMD) simulations to access structural properties at finite temperature, and combined our ab initio data with a 2-4-6 Landau-Falk expansion of the free energy [12, 13] to characterize the nature of reversible MTs and suggest necessary conditions to dis...