The thermodynamic definition of entropy can be extended to nonequilibrium systems based on its relation to information. To apply this definition in practice requires access to the physical system's microstates, which may be prohibitively inefficient to sample or difficult to obtain experimentally. It is beneficial, therefore, to relate the entropy to other integrated properties which are accessible out of equilibrium. We focus on the structure factor, which describes the spatial correlations of density fluctuations and can be directly measured by scattering. The information gained by a given structure factor regarding an otherwise unknown system provides an upper bound for the system's entropy. We find that the maximum-entropy model corresponds to an equilibrium system with an effective pair-interaction. Approximate closed-form relations for the effective pair-potential and the resulting entropy in terms of the structure factor are obtained. As examples, the relations are used to estimate the entropy of an exactly solvable model and two simulated systems out of equilibrium. The focus is on low-dimensional examples, where our method, as well as a recently proposed compression-based one, can be tested against a rigorous direct-sampling technique. The entropy inferred from the structure factor is found to be consistent with the other methods, superior for larger system sizes, and accurate in identifying global transitions. Our approach allows for extensions of the theory to more complex systems and to higher-order correlations.
Inferring entropy production in many-body systems using nonequilibrium maximum entropy
BCAM -- Basque Center for Applied Mathematics（巴斯克应用数学中心）；Universal Biology Institute（通用生物学研究所）；Department of Physics（物理系）；ICREA-Complex Systems Lab（ICREA复杂系统实验室）
Inference, Prediction, and Entropy-Rate Estimation of Continuous-time, Discrete-event Processes
W. M. Keck Science Department of Pitzer, Scripps, and Claremont McKenna College（皮泽学院、斯克里普斯学院和克莱蒙特·麦肯纳学院W.M.凯克科学系）；University of California at Davis（加州大学戴维斯分校）
Inferring Pattern and Disorder in Close-Packed Structures from X-ray Diffraction Studies, Part II: Structure and Intrinsic Computation in Zinc Sulphide
在本系列的前一篇文章[D. P. Varn，G. S. Canright和J. P. Crutchfield在《物理评论B》中提交了]我们详细介绍了一种程序--ε机光谱重建--以发现和分析X射线衍射光谱中揭示的密堆积结构中的图案和无序。我们认为，这种计算力学的方法是更普遍的比目前的替代理论，故障模型，它提供了一个独特的表征目前的混乱。我们证明了计算力学对四个原型光谱的有效性，发现它能够使用ε机表示来恢复底层模块层堆叠的统计描述。在这里，我们使用这个程序来分析结构和无序在四个以前发表的硫化锌衍射光谱。我们选择硫化锌不仅是因为这种材料在努力发展对多型性的理解方面引起了理论上的兴趣，而且还因为它显示固态相变并且实验数据可用。
Inferring Pattern and Disorder in Close-Packed Structures from X-ray Diffraction Studies, Part I: epsilon-Machine Spectral Reconstruction Theory
在最近的一份出版物[D。P. Varn，G. S. Canright和J. P. Crutchfield，Phys. Rev. B { \bf 66}：17，156（2002）]我们引入了一种新技术，用于直接从其衍射光谱发现和描述密堆积结构（CPS）中的平面无序。在这里，我们提供了这些结果背后的理论发展，适应计算力学来描述材料中的一维结构。通过对比，我们给出了一个详细的分析，目前的替代方法，故障模型（FM），并提供了一些批评。然后，我们证明，堆叠序列的计算力学描述-在一个ε机的形式-提供了最小的和唯一的描述的晶体，无论是有序的，无序的，或一些组合。我们发现，我们可以检测和描述任何数量的无序，以及各种晶体结构的混合物。这种方法的基础是一种新的方法ε机重建，使用关联函数估计从衍射光谱，而不是序列的微观配置，通常用于其他领域。其结果是，这里开发的方法可以适用于广泛的实验系统，其中光谱数据是可用的。
