Abstract Rapid solidification is a relevant physical phenomenon in material sciences, whose theoretical analysis requires going beyond the limits of local equilibrium statistical physics and thermodynamics and, in particular, taking account of ergodicity breaking and of generalized formulation of thermodynamics. The ergodicity breaking is related to the time symmetry breaking and to the presence of some kinds of fluxes and gradient flows making that an average of microscopic variables along time is different than an average over some chosen statistical ensemble. In fast processes, this is due, for instance, to the fact that the system has no time enough to explore the whole region of possible microscopic states in the phase space. Similarly to this, systems submitted to strong fluxes may have no time for reaching the whole phase space in local bulks during observable macroscopic time. Rapid solidification, ergodicity breaking and extended thermodynamics actually make a conceptually novel combination in the present overview: ergodicity breaking is expressed in general terms and then extended thermodynamics is formulated as a particular phenomenological expression and applied to describe the dynamics of the phenomenon. Using the formalism of micro- and meso-scopic dynamics we introduce a general view on non-ergodic fast transitions and provide a simplest description of a continuum theory based on the system of hyperbolic equations applicable to rapid solidification. Analysis of non-equilibrium effects, including interface kinetics, solute trapping and solute drag, is presented with their effect on the rapidly moving solid–liquid interface. Special attention is paid to the theory predictions compared with the kinetics obtained in experiments on samples processed by electromagnetic levitation facility and in molecular dynamics simulation.

中文翻译：

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快速凝固为非遍历现象

摘要 快速凝固是材料科学中的一个相关物理现象，其理论分析需要超越局部平衡统计物理和热力学的限制，特别是考虑遍历性破缺和热力学的广义表述。遍历性破坏与时间对称性破坏以及某些类型的通量和梯度流的存在有关，这使得随时间变化的微观变量的平均值与某些选定统计集合的平均值不同。例如，在快速过程中，这是由于系统没有足够的时间来探索相空间中可能的微观状态的整个区域。与此类似，在可观察的宏观时间内，承受强通量的系统可能没有时间到达局部体的整个相空间。快速凝固、遍历性破坏和扩展热力学实际上在本概述中形成了一个概念上新颖的组合：遍历性破坏以一般术语表示，然后扩展热力学被表述为特定的现象学表达式并应用于描述现象的动力学。使用微观和细观动力学的形式主义，我们介绍了非遍历快速转变的一般观点，并提供了基于适用于快速凝固的双曲方程系统的连续统理论的最简单描述。非平衡效应分析，包括界面动力学、溶质捕获和溶质阻力，展示了它们对快速移动的固液界面的影响。特别注意与在电磁悬浮设备处理的样品实验和分子动力学模拟中获得的动力学相比的理论预测。