More than a century has passed since van't Hoff and Arrhenius formulated their celebrated rate theories, but there are still elusive aspects in the temperature-dependent phase transition kinetics of molecular systems. Here I present a theory based on microcanonical thermostatistics that establishes a simple and direct temperature dependence for all rate constants, including the forward and the reverse rate constants, the equilibrium constant, and the nucleation rate. By considering a generic model that mimic the microcanonical temperature of molecular systems in a region close to a first-order phase transition, I obtain shape-free relations between kinetics and thermodynamics physical quantities which are validated through stochastic simulations. Additionally, the rate theory is applied to results obtained from protein folding and ice nucleation experiments, demonstrating that the expressions derived here can be used to describe the experimental data of a wide range of molecular systems.

中文翻译：

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来自微正则热力学的一阶相变动力学

自 van't Hoff 和 A​​rrhenius 制定他们著名的速率理论以来已经过去了一个多世纪，但分子系统的温度相关相变动力学仍然存在难以捉摸的方面。在这里，我提出了一个基于微正则热力学的理论，该理论为所有速率常数建立了简单而直接的温度依赖性，包括正向和反向速率常数、平衡常数和成核速率。通过考虑在接近一级相变的区域模拟分子系统微正则温度的通用模型，我获得了动力学和热力学物理量之间的无形状关系，这些关系通过随机模拟得到验证。此外，