Complex Systems Research Group and Centre for Complex Systems, Faculty of Engineering and IT, The University of Sydney, Sydney, NSW 2006, Australia.
Phys Rev E. 2018 Jan;97(1-1):012120. doi: 10.1103/PhysRevE.97.012120.
We study self-organization of collective motion as a thermodynamic phenomenon in the context of the first law of thermodynamics. It is expected that the coherent ordered motion typically self-organises in the presence of changes in the (generalized) internal energy and of (generalized) work done on, or extracted from, the system. We aim to explicitly quantify changes in these two quantities in a system of simulated self-propelled particles and contrast them with changes in the system's configuration entropy. In doing so, we adapt a thermodynamic formulation of the curvatures of the internal energy and the work, with respect to two parameters that control the particles' alignment. This allows us to systematically investigate the behavior of the system by varying the two control parameters to drive the system across a kinetic phase transition. Our results identify critical regimes and show that during the phase transition, where the configuration entropy of the system decreases, the rates of change of the work and of the internal energy also decrease, while their curvatures diverge. Importantly, the reduction of entropy achieved through expenditure of work is shown to peak at criticality. We relate this both to a thermodynamic efficiency and the significance of the increased order with respect to a computational path. Additionally, this study provides an information-geometric interpretation of the curvature of the internal energy as the difference between two curvatures: the curvature of the free entropy, captured by the Fisher information, and the curvature of the configuration entropy.
我们从热力学第一定律的角度研究了集体运动自组织作为热力学现象。预计在（广义）内能变化以及对系统做功或从系统提取功的情况下，典型的连贯有序运动将自组织。我们旨在通过对比系统构型熵的变化，明确量化模拟自推进粒子系统中这两个量的变化。为此，我们采用了一种热力学方法来对内能和功的曲率进行表述，这两个参数控制着粒子的对齐方式。这使我们能够通过改变两个控制参数来系统地研究系统的行为，从而使系统经历一个动力学相变。我们的结果确定了关键状态，并表明在系统构型熵减小的相变期间，功和内能的变化率也减小，而它们的曲率则发散。重要的是，通过做功实现的熵减少在临界点达到峰值。我们将这一点与热力学效率以及相对于计算路径的增加秩序的重要性联系起来。此外，本研究还为内能的曲率提供了一种信息几何解释，即将其表示为两个曲率之间的差异：自由熵的曲率，由 Fisher 信息捕获，以及构型熵的曲率。
