The accurate prediction of phase diagrams is of central importance for both
the fundamental understanding of materials as well as for technological
applications in material sciences. However, the computational prediction of the
relative stability between phases based on their free energy is a daunting
task, as traditional free energy estimators require a large amount of
simulation data to obtain uncorrelated equilibrium samples over a grid of
thermodynamic states. In this work, we develop deep generative machine learning
models for entire phase diagrams, employing normalizing flows conditioned on
the thermodynamic states, e.g., temperature and pressure, that they map to. By
training a single normalizing flow to transform the equilibrium distribution
sampled at only one reference thermodynamic state to a wide range of target
temperatures and pressures, we can efficiently generate equilibrium samples
across the entire phase diagram. Using a permutation-equivariant architecture
allows us, thereby, to treat solid and liquid phases on the same footing. We
demonstrate our approach by predicting the solid-liquid coexistence line for a
Lennard-Jones system in excellent agreement with state-of-the-art free energy
methods while significantly reducing the number of energy evaluations needed.

通过深度生成机器学习模型和热力学状态的条件正则化流，我们可以高效地生成整个相图的平衡样本，并在预测固液共存线时降低所需能量评估数量。

带条件的正规化流方法高效映射相图

Efficient mapping of phase diagrams with conditional normalizing flows

The multistate Bennett acceptance ratio (MBAR) method is a prevalent approach
for computing free energies of thermodynamic states. In this work, we introduce
BayesMBAR, a Bayesian generalization of the MBAR method. By integrating
configurations sampled from thermodynamic states with a prior distribution,
BayesMBAR computes a posterior distribution of free energies. Using the
posterior distribution, we derive free energy estimations and compute their
associated uncertainties. Notably, when a uniform prior distribution is used,
BayesMBAR recovers the MBAR's result but provides more accurate uncertainty
estimates. Additionally, when prior knowledge about free energies is available,
BayesMBAR can incorporate this information into the estimation procedure by
using non-uniform prior distributions. As an example, we show that, by
incorporating the prior knowledge about the smoothness of free energy surfaces,
BayesMBAR provides more accurate estimates than the MBAR method. Given MBAR's
widespread use in free energy calculations, we anticipate BayesMBAR to be an
essential tool in various applications of free energy calculations.

引入 BayesMBAR 作为 MBAR 方法的贝叶斯推广，在计算热力学状态的自由能值时，通过将采样自热力学状态的构型与先验分布整合，计算出自由能的后验分布，并通过后验分布得出自由能估计和估计误差。BayesMBAR 能够提供比 MBAR 方法更准确的不确定性估计，同时也可以整合关于自由能的先验知识，提供更准确的估计结果，并有望成为自由能计算的重要工具。

贝叶斯多状态贝内特接受比率方法

Bayesian Multistate Bennett Acceptance Ratio Methods

A fundamental problem in modern thermodynamics is how a molecular-scale
machine performs useful work, while operating away from thermal equilibrium
without excessive dissipation. To this end, we derive a friction tensor that
induces a Riemannian manifold on the space of thermodynamic states. Within the
linear-response regime, this metric structure controls the dissipation of
finite-time transformations, and bestows optimal protocols with many useful
properties. We discuss the connection to the existing thermodynamic length
formalism, and demonstrate the utility of this metric by solving for optimal
control parameter protocols in a simple nonequilibrium model.

研究了现代热力学中一个基本问题：如何在热力学非平衡情况下，分子级机器执行有用的工作而没有过多的能量耗散。提出了一种摩擦张量，并在热力学状态空间上引入了黎曼流形，控制了有限时间的转化过程中的能量耗散，并为最优控制提供了各种实际应用。通过解决一个简单的非平衡模型中的最优控制参数来证明这种度量的实用性。