Teles Tarcísio N, Farias Calvin A F, Pakter Renato, Levin Yan
Grupo de Física de Feixes, Universidade Federal de Ciências da Saúde de Porto Alegre (UFCSPA), Porto Alegre 90050-170, RS, Brazil.
Instituto de Física, Universidade Federal do Rio Grande do Sul (UFRGS), Caixa Postal 15051, Porto Alegre 91501-970, RS, Brazil.
Entropy (Basel). 2023 Sep 25;25(10):1379. doi: 10.3390/e25101379.
We present a Monte Carlo approach that allows us to easily implement Lynden-Bell (LB) entropy maximization for an arbitrary initial particle distribution. The direct maximization of LB entropy for an arbitrary initial distribution requires an infinite number of Lagrange multipliers to account for the Casimir invariants. This has restricted studies of Lynden-Bell's violent relaxation theory to only a very small class of initial conditions of a very simple waterbag form, for which the entropy maximization can be performed numerically. In the present approach, an arbitrary initial distribution is discretized into density levels which are then evolved using an efficient Monte Carlo algorithm towards the final equilibrium state. A comparison is also made between the LB equilibrium and explicit Molecular Dynamics simulations. We find that for most initial distributions, relaxation is incomplete and the system is not able to reach the state of maximum LB entropy. In particular, we see that the tail of the stationary particle distribution is very different from the one predicted by the theory of violent relaxation, with a hard cutoff instead of an algebraic decay predicted by LB's theory.
我们提出了一种蒙特卡罗方法，它使我们能够轻松地对任意初始粒子分布实现林登 - 贝尔（LB）熵最大化。对于任意初始分布直接最大化LB熵需要无穷多个拉格朗日乘数来考虑卡西米尔不变量。这将林登 - 贝尔剧烈弛豫理论的研究限制在非常简单的水袋形式的极少数初始条件上，对于这些条件，可以通过数值方法进行熵最大化。在当前方法中，将任意初始分布离散为密度水平，然后使用高效的蒙特卡罗算法朝着最终平衡态演化。我们还对LB平衡和显式分子动力学模拟进行了比较。我们发现，对于大多数初始分布，弛豫是不完全的，系统无法达到最大LB熵状态。特别是，我们看到稳态粒子分布的尾部与剧烈弛豫理论预测的非常不同，具有硬截断而不是LB理论预测的代数衰减。
