Nandi Ujjwal Kumar, Patel Palak, Moid Mohd, Nandi Manoj Kumar, Sengupta Shiladitya, Karmakar Smarajit, Maiti Prabal K, Dasgupta Chandan, Maitra Bhattacharyya Sarika
Polymer Science and Engineering Division, CSIR-National Chemical Laboratory, Pune 411008, India.
Centre for Condensed Matter Theory, Department of Physics, Indian Institute of Science, Bangalore 560012, India.
J Chem Phys. 2022 Jan 7;156(1):014503. doi: 10.1063/5.0065668.
A recent study introduced a novel mean-field model system where each particle over and above the interaction with its regular neighbors interacts with k extra pseudo-neighbors. Here, we present an extensive study of thermodynamics and its correlation with the dynamics of this system. We surprisingly find that the well-known thermodynamic integration (TI) method of calculating the entropy provides unphysical results. It predicts vanishing of the configurational entropy at temperatures close to the onset temperature of the system and negative values of the configurational entropy at lower temperatures. Interestingly, well below the temperature at which the configurational entropy vanishes, both the collective and the single-particle dynamics of the system show complete relaxation. Negative values of the configurational entropy are unphysical, and complete relaxation when the configurational entropy is zero violates the prediction of the random first-order transition theory (RFOT). However, the entropy calculated using the two-phase thermodynamics (2PT) method remains positive at all temperatures for which we can equilibrate the system, and its values are consistent with RFOT predictions. We find that with an increase in k, the difference in the entropy computed using the two methods increases. A similar effect is also observed for a system where a randomly selected fraction of the particles are pinned in their positions in the equilibrated liquid. We show that the difference in entropy calculated via the 2PT and TI methods increases with pinning density.
最近的一项研究引入了一种新颖的平均场模型系统，其中每个粒子除了与其常规邻居相互作用外，还与k个额外的伪邻居相互作用。在此，我们对该系统的热力学及其与动力学的相关性进行了广泛研究。我们惊讶地发现，计算熵的著名热力学积分（TI）方法给出了不符合物理实际的结果。它预测在接近系统起始温度的温度下构型熵消失，而在较低温度下构型熵为负值。有趣的是，在构型熵消失温度以下很远的地方，系统的集体动力学和单粒子动力学都显示出完全弛豫。构型熵为负值是不符合物理实际的，并且当构型熵为零时的完全弛豫违反了随机一阶转变理论（RFOT）的预测。然而，使用两相热力学（2PT）方法计算的熵在我们能够使系统达到平衡的所有温度下都保持为正，并且其值与RFOT预测一致。我们发现，随着k的增加，使用这两种方法计算的熵的差异增大。对于一个在平衡液体中随机选择一部分粒子固定在其位置的系统，也观察到了类似的效应。我们表明，通过2PT和TI方法计算的熵的差异随着固定密度的增加而增大。
