论文标题
kullback-自由冷却颗粒气的发散
Kullback--Leibler Divergence of a Freely Cooling Granular Gas
论文作者
论文摘要
找到与隔离的自由冷却颗粒气体相关的适当的熵样Lyapunov功能是仍然无法解决的挑战。原始的$ h $ theorem假设在这里不适合，$ h $功能提出了一些其他措施问题，这些问题是由kullback-leibler Divergence（KLD）从实际分布中解决的。 KLD中参考分布的正确选择对于后者有资格或不作为Lyapunov功能，渐近的“同质冷却状态”（HCS）分布是潜在的候选者。由于缺乏正式的证明远离准循环限制，这项工作的目的是支持这种猜想，这是通过分子动力学模拟对无弹性硬盘和领域的分子动力学模拟的辅助，以换成恢复系数（$α$）以及不同初始条件。我们的结果拒绝麦克斯韦分布作为可能的参考，而它们加强了HCS。此外，KLD用于测量使用前者而不是后者丢失的信息量，从而揭示了$α$的非单调依赖性。
Finding the proper entropy-like Lyapunov functional associated with the inelastic Boltzmann equation for an isolated freely cooling granular gas is a still unsolved challenge. The original $H$-theorem hypotheses do not fit here and the $H$-functional presents some additional measure problems that are solved by the Kullback--Leibler divergence (KLD) of a reference velocity distribution function from the actual distribution. The right choice of the reference distribution in the KLD is crucial for the latter to qualify or not as a Lyapunov functional, the asymptotic "homogeneous cooling state" (HCS) distribution being a potential candidate. Due to the lack of a formal proof far from the quasielastic limit, the aim of this work is to support this conjecture aided by molecular dynamics simulations of inelastic hard disks and spheres in a wide range of values for the coefficient of restitution ($α$) and for different initial conditions. Our results reject the Maxwellian distribution as a possible reference, whereas they reinforce the HCS one. Moreover, the KLD is used to measure the amount of information lost on using the former rather than the latter, revealing a non-monotonic dependence with $α$.
