论文标题
从头开始研究大型系统统计力学中的玻尔兹曼处方的数值研究
Numerical studies for an ab initio investigation into the Boltzmann prescription in statistical mechanics of large systems
论文作者
论文摘要
我们提出了有关统计力学对大型系统的有效性问题的数值研究，并解决了能源扩张是否意味着玻尔兹曼熵的扩张性的问题。这个问题的重要性源于以下事实：某些调查人员目前认为它是开放的，但其他人已经解决了。我们报告了具有远距离交互和短程相互作用的类似气体的汉密尔顿系统的从头算结果，这些模拟明确考虑了整个希尔伯特空间的$ 2^{30} \ 10^9 $状态。该技术的基础是蒙特卡洛算法。尽管使用的数量很大，但仔细的检查表明，所研究的系统仍然太小，无法独特地解决提出的问题。因此，概述的新方法代表了解决第一原则的第一步。还提供一般理论评论以补充数值研究。
We present numerical investigations into the question of the validity of the Boltzmann prescription in Statistical Mechanics for large systems, addressing the issue of whether extensivity of energy implies the extensivity of the Boltzmann entropy. The importance of the question stems from the fact that it is currently considered open by some investigators but quite settled by others. We report ab initio results for gas-like Hamiltonian systems with long-range as well as short-range interactions, based on simulations that explicitly consider more than $2^{30} \approx 10^9$ states of the full Hilbert space. The basis of the technique is Monte Carlo algorithms. Despite the largeness of the numbers used, careful inspection shows that the systems studied are still too small to settle uniquely the issues raised. Therefore, the new approach outlined represents a first step in addressing on first principles the question of non-extensive statistical mechanics. General theoretical comments are also supplied to supplement the numerical investigations.
