做材料模拟的朋友可以看看，这个TIP把自由能算得又快又准，还能直接找相变点，省掉传统系综平均的麻烦。
该论文提出热力学原子间势(TIP)，将原子间势从静态能量扩展为热力学一致的吉布斯自由能模型，可通过自动微分得到热力学响应。作者用通用势UMA实现TIP[UMA]，在从准谐近似到分子动力学精度的自由能数据上训练，并校准到高分辨率计算或实验。单次评估即可返回晶体状态方程，并定位竞争相之间的相变，包括动态稳定相。微调后还能扩展到合金溶解度极限和混溶间隙，为高通量有限温度相稳定性研究铺路。
Universal Thermodynamic Interatomic Potentials for Crystalline Materials
Free energies govern solid-state phase stability, yet computational materials discovery still relies largely on ground-state energies because free energy calculations require ensemble averages. We introduce the thermodynamic interatomic potential (TIP), which extends an interatomic potential from its static energy to a thermodynamically consistent Gibbs free energy model, with thermodynamic responses following from temperature and pressure by automatic differentiation. We implement TIP[UMA] using the universal potential UMA, train it on free energies from quasi-harmonic to molecular dynamics fidelity, and calibrate it to higher-resolution calculations or experiment. From a single evaluation, it returns the equation of state of a crystal and locates phase transitions among competing branches, including dynamically stabilized phases. Fine-tuning extends the model to alloy solubility limits and miscibility gaps. TIP makes the free energy as accessible as the potential energy, opening finite-temperature phase stability to high-throughput discovery.