标题： 指数倾斜热力学映射（expTM）：在温度、压力和化学势范围内预测相变 显示英文标题

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

摘要： 预测和表征相变对于理解诸如结晶、蛋白质折叠等一般的物理现象至关重要。 然而，直接观察相变并不总是容易的，通常只能在远离相边界的地方获得有限的观测数据，并且是在某些特定的热力学条件下测得的。 在本研究中，我们提出了一种由统计物理和生成人工智能驱动的框架，该框架可以利用这些有限的信息，在任意热力学条件下生成不同相的样本，我们将其命名为指数倾斜热力学图（expTM）。 核心思想是将收集到的数据映射到一个易于处理的简单先验分布，该分布表示为指数倾斜的高斯分布。 我们展示了先验分布的方差和均值如何与温度、压力和化学势等一对热力学控制变量相关联。 这使我们能够在任何控制变量值下生成热力学正确的样本。 为了展示该方法的实际适用性，我们使用expTM对巨正则系综下的格子气体模型进行采样，在不同的化学势和温度下捕捉相变。 我们进一步展示了expTM如何建模等温等压系综，并据此预测不同压力条件下的CO2的不同相。 这两个例子都是在远离相边界的数据上训练的。 这些结果确立了expTM作为一种强大的工具，用于在只需要少量观测的情况下理解各种热力学条件下的相变。 显示英文摘要

摘要： 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.