Free energy determines which phase of a substance is stable under given conditions, but computational chemistry still relies mostly on energies at zero temperature. The reason is simple: free energy requires averaging over a thermal ensemble—a set of atomic configurations vibrating at a given temperature. This is expensive: a single thermodynamic integration calculation can take hours on a supercomputer. Alongside this work, efforts to accelerate such calculations fall into two camps: some build fast surrogates for specific systems, others train universal potentials that still require resampling for each new structure. The authors take a third path—they train a model to output free energy directly, without additional sampling.
TIP is based on splitting the free energy into a static part at zero temperature and a thermodynamic remainder that the model learns. The static energy comes from a frozen universal potential, UMA, while the remainder is predicted by a lightweight neural network that, given atomic features and conditions (temperature, pressure), outputs an analytic form for the free energy. This form is assembled from physically meaningful terms: an Einstein oscillator for vibrations and a Murnaghan equation of state for volume. Training proceeds in three stages: first on cheap quasiharmonic calculations (120,000 structures), then on accurate free energies from nonequilibrium molecular dynamics (95,000 points), and finally calibration on experimental data—heat capacities, equations of state, and solubility limits.
On the validation set, the model achieves a median free energy error of 10.3 meV/atom—several times better than previous descriptor-based models (46–60 meV/atom). For 255 stoichiometric compounds from the NIST–JANAF tables, the heat capacity error is 1.94 J/(K·mol atoms), and the standard entropy error is 2.28 J/(K·mol atoms). The model predicts polymorphic transitions in titanium, hafnium, and CaSiO3 to within 250 K, including phases that lack a stable harmonic reference at zero temperature. After calibration on experimental data, the model corrects the systematic volume overestimation inherited from PBE and recovers the correct phase diagram of SiO2. For alloys, TIP reproduces the solubility of scandium in aluminum and the miscibility gap of Au–Pt, fitting experimental curves via differentiable resampling.
This work fits into the broader effort to create universal thermodynamic surrogates, but it stands out by not requiring repeated statistical sampling for each new structure. Unlike cluster expansions tied to a specific lattice and CALPHAD assessments that need manual fitting for each system, TIP transfers knowledge across chemical elements and phases. It is the first model that combines the chemical universality of machine-learned potentials with direct prediction of free energy and its derivatives—volume, entropy, heat capacity, bulk modulus—from a single calculation.
The model can be extended to include magnetic and electronic contributions to entropy by adding corresponding terms to the analytic form or by feeding in charge and spin state features. Another direction is incorporating defects, surfaces, and interfaces, which require separate thermodynamic references. For liquids, new reference states and representations independent of the ordered crystalline branch will be needed. In the long run, this paves the way toward a differentiable foundational thermodynamic model calibrated on first principles and experiment.
The method will accelerate high-throughput screening of materials for batteries, thermoelectrics, alloys, and geological phases where stability at operating temperatures and pressures is critical.
The authors plan to improve the convergence of reference free energy calculations, expand coverage across chemical elements and pressures, and add magnetic and electronic degrees of freedom.
In materials science, predicting metastable phases and kinetically hindered transitions remains an open problem: free energy is only half the answer—we also need barriers between branches. TIP provides accurate free energy branches but does not describe transition paths between them. Another unresolved challenge is accounting for configurational entropy in multicomponent systems with substitutional disorder: here the model relies on expensive sampling that one would like to replace with direct prediction.
This section is addressed to the author of the paper and their colleagues. Neighbouring works were found by meaning-based search across our archive, not by word overlap. We do not review: we show the field around the work.
What the work does
The authors introduce a thermodynamic interatomic potential (TIP) that predicts the Gibbs free energy as a function of temperature and pressure from a single static structure. The model is trained on data from three levels of accuracy: the quasi-harmonic approximation, non-equilibrium molecular dynamics, and experimental measurements. TIP reproduces equations of state, heat capacities, polymorphic transitions, and solubility limits of alloys with a free energy error of about 10 meV/atom.
Where its strength is
The key strength of the work lies in avoiding resampling: the free energy is computed directly, making it as accessible as potential energy. This is achieved through a physically motivated architecture and multi-level training, including calibration on experimental data.
Where it could go next
Worth trying
Why this may matter
If the approach can be extended to a wide class of materials, it could make thermodynamic calculations routine in high-throughput screening, bridging the gap between zero-temperature energy predictions and real operating conditions.
Nearby works in our archive
The closest work in the archive sits at 0.64 by meaning — the usual level for our corpus.
The model predicts free energy in 0.1 seconds per structure — a hundred thousand times faster than nonequilibrium molecular dynamics and a thousand times faster than quasiharmonic calculations.