Exponentially Tilted Thermodynamic Maps (expTM): Predicting Phase Transitions Across Temperature, Pressure, and Chemical Potential

Predicting and characterizing phase transitions is crucial for understanding generic physical phenomena such as crystallization, protein folding and others. However, directly observing phase transitions is not always easy, and often one has limited observations far from the phase boundary and measured under some specific thermodynamic conditions. In this study, we propose a statistical physics and Generative AI driven framework that can take such limited information to generate samples of different phases under arbitrary thermodynamic conditions, which we name Exponentially Tilted Thermodynamic Maps (expTM). The central idea is to map collected data into a tractable simple prior expressed as an exponentially tilted Gaussian. We demonstrate how the variance and mean of the prior can be correlated with pairs of thermodynamic control variables, including temperature, pressure, and chemical potential. This gives us the ability to generate thermodynamically correct samples under any values of the control variables. To demonstrate the practical applicability of this approach, we use expTM to sample the lattice gas models with the Grand Canonical ensemble, capturing phase transitions under varying chemical potentials and temperatures. We further demonstrate how expTM can model the isothermal-isobaric ensemble, with which we predict different phases of CO2 under varying pressure conditions. Both examples are trained on very limited data far from the phase boundary. These results establish expTM as a robust tool for understanding phase transitions across diverse thermodynamic conditions requiring only a small number of observations.