论文标题
MA的方法计算熵的$ k $ -mers在正方形晶格上的系统
Calculating entropy by Ma's method for a system of $k$-mers on a square lattice
论文作者
论文摘要
Boltzmann的熵是任何动态系统的重要特征。对于大型系统，很难直接计算Boltzmann的熵作为当前宏观物质的微骨总数的对数。在研究$ k $ -mers（相邻$ k $相邻单元格的线性片段）的扩散的情况下，计数可能的微晶格的复杂性随着系统中的$ k $ - 米数的数量而增长。解决此问题的明显解决方案是仅获得熵的估计值，因为这是更快的计算速度。 2D滑动窗口技术可用于将晶格上的$ k $ - 米尔系统分为子系统。我们使用MA的“巧合”方法来估计此类子系统可能的状态总数。在这项研究中，通过实验和理论上的简单组合模型研究了MA方法的准确性。我们确定该方案的“巧合”的定义会导致更高的准确性。如果忽略了$ k $ - 米之间的复杂交互，则MA对$ K $ -MERS系统可能状态数量的估计与使用“幼稚”方法获得的估计值息息相关。
Boltzmann's entropy is an important feature of any dynamic system. Calculating Boltzmann's entropy directly as the logarithm of the total number of microstates for a current macrostate is difficult for large systems. In the case of studying the diffusion of $k$-mers (linear segments of $k$ adjacent cells) on a lattice, the complexity of counting the possible microstates grows exponentially with the number of $k$-mers in the system. The obvious solution to this problem is to obtain only an estimate for the entropy, as this is faster to calculate. The 2D sliding window technique can be used to divide a system of $k$-mers on a lattice into subsystems. We use Ma's "coincidence" method to estimate the total number of possible states for such subsystems. In this study, the accuracy of Ma's method is studied in a simple combinatory model, both experimentally and theoretically. We determine which definition of "coincidence" for this scheme leads to greater accuracy. Where complex interactions between $k$-mers are ignored, Ma's estimate of the number of possible states for a system of $k$-mers correlates well with the estimate obtained using a "naive" method.
