A different approach to introducing statistical mechanics
A different approach to introducing statistical mechanics
复制标题
引入统计力学的不同方法
DOI：
10.1119/1.18490
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发表时间：
2015
影响因子：
0.9
通讯作者：
D. V. Schroeder
中科院分区：
文献类型：
--
作者：
T. Moore;D. V. Schroeder
统计力学的基本概念（微观状态、多重性）非常简单，但要理解第二定律如何从这些概念中产生，需要处理繁琐的大数。为了避免陷入数学困境，人们可以对一个简单的模型系统（例如爱因斯坦固体——一组相同的量子谐振子的集合）进行数值计算。计算机电子表格程序或类似软件可以计算包含数百个振荡器和能量单位的系统所需的组合函数。当两个这样的系统可以交换能量时，人们会立即发现某些配置比其他配置更有可能。两个系统的熵与能量图可用于激发温度的理论定义 T=(∂S/∂U)−1，从而弥合经典熵方法和统计方法之间的差距。进一步的电子表格练习可用于计算爱因斯坦固体的热容，研究......
The basic notions of statistical mechanics (microstates, multiplicities) are quite simple, but understanding how the second law arises from these ideas requires working with cumbersomely large numbers. To avoid getting bogged down in mathematics, one can compute multiplicities numerically for a simple model system such as an Einstein solid—a collection of identical quantum harmonic oscillators. A computer spreadsheet program or comparable software can compute the required combinatoric functions for systems containing a few hundred oscillators and units of energy. When two such systems can exchange energy, one immediately sees that some configurations are overwhelmingly more probable than others. Graphs of entropy vs. energy for the two systems can be used to motivate the theoretical definition of temperature, T=(∂S/∂U)−1, thus bridging the gap between the classical and statistical approaches to entropy. Further spreadsheet exercises can be used to compute the heat capacity of an Einstein solid, study the ...