论文标题
玻尔茨曼在自由膨胀相互作用的理想气体中的熵
Boltzmann's entropy during free expansion of an interacting ideal gas
论文作者
论文摘要
在这项工作中，我们研究了Boltzmann熵的演变，这是在盒子内的一维相互作用气体的自由膨胀的背景下。 Boltzmann的熵是针对单个微晶体定义的，并由具有相同的大颗粒物值的微晶体占据的相位空间体积给出。我们证明了鲍尔茨曼熵生长中典型性的概念，以实现两种宏观变量的选择 - 单个粒子相空间分布和流体动力场。由于相互作用的存在，观察到这两个熵的生长曲线都会收敛到单调增加的限制曲线，在采取适当的限制范围内，具有较大的系统尺寸和小的粗砂尺度。此外，我们观察到，两种熵选择的限制生长曲线与局部热平衡所暗示的相同。我们还讨论了与有限的大小和有限的粗制量表有关的问题，这些问题引起了有趣的特征，例如熵生长曲线中的振荡。我们还讨论在流体动力场中观察到的冲击。
In this work we study the evolution of Boltzmann's entropy in the context of free expansion of a one dimensional interacting gas inside a box. Boltzmann's entropy is defined for single microstates and is given by the phase-space volume occupied by microstates with the same value of macrovariables which are coarse-grained physical observables. We demonstrate the idea of typicality in the growth of the Boltzmann's entropy for two choices of macro-variables -- the single particle phase space distribution and the hydrodynamic fields. Due to the presence of interaction, the growth curves for both these entropies are observed to converge to a monotonically increasing limiting curve, on taking the appropriate order of limits, of large system size and small coarse graining scale. Moreover, we observe that the limiting growth curves for the two choices of entropies are identical as implied by local thermal equilibrium. We also discuss issues related to finite size and finite coarse gaining scale which lead interesting features such as oscillations in the entropy growth curve. We also discuss shocks observed in the hydrodynamic fields.
