Korbel Jan, Lindner Simon David, Hanel Rudolf, Thurner Stefan
Section for the Science of Complex Systems, CeMSIIS, Medical University of Vienna, Vienna, Austria.
Complexity Science Hub Vienna, Vienna, Austria.
Nat Commun. 2021 Feb 18;12(1):1127. doi: 10.1038/s41467-021-21272-7.
Structure-forming systems are ubiquitous in nature, ranging from atoms building molecules to self-assembly of colloidal amphibolic particles. The understanding of the underlying thermodynamics of such systems remains an important problem. Here, we derive the entropy for structure-forming systems that differs from Boltzmann-Gibbs entropy by a term that explicitly captures clustered states. For large systems and low concentrations the approach is equivalent to the grand-canonical ensemble; for small systems we find significant deviations. We derive the detailed fluctuation theorem and Crooks' work fluctuation theorem for structure-forming systems. The connection to the theory of particle self-assembly is discussed. We apply the results to several physical systems. We present the phase diagram for patchy particles described by the Kern-Frenkel potential. We show that the Curie-Weiss model with molecule structures exhibits a first-order phase transition.
结构形成系统在自然界中无处不在，从构建分子的原子到胶体两性粒子的自组装。对这类系统潜在热力学的理解仍然是一个重要问题。在此，我们推导了结构形成系统的熵，它与玻尔兹曼 - 吉布斯熵的区别在于有一项明确捕捉了聚集态。对于大系统和低浓度，该方法等同于巨正则系综；对于小系统，我们发现有显著偏差。我们推导了结构形成系统的详细涨落定理和克鲁克斯功涨落定理。讨论了与粒子自组装理论的联系。我们将结果应用于几个物理系统。我们给出了由克恩 - 弗伦克尔势描述的补丁粒子的相图。我们表明具有分子结构的居里 - 外斯模型表现出一级相变。
