论文标题
小型热力学系统中的准静态分解和吉布斯阶乘
Quasi-static decomposition and the Gibbs factorial in small thermodynamic system
论文作者
论文摘要
对于与热浴接触的小型热力学系统，我们通过施加以下两个条件来确定自由能。首先，任何配置变化中的准静态工作都等于自由能差。其次，自由能的温度依赖性满足了吉布斯 - 赫尔莫尔兹的关系。我们发现，这些先决条件独特地导致了由$ n $互动相同的粒子组成的经典系统的自由能，最多与$ n $成比例的添加剂常数。因此，除了Gibbs-Boltzmann因子的相空间集成外，自由能还包含Gibbs阶乘$ n！$。推导的关键步骤是构建小型热力学系统的准静态分解。
For small thermodynamic systems in contact with a heat bath, we determine the free energy by imposing the following two conditions. First, the quasi-static work in any configuration change is equal to the free energy difference. Second, the temperature dependence of the free energy satisfies the Gibbs-Helmholtz relation. We find that these prerequisites uniquely lead to the free energy of a classical system consisting of $N$-interacting identical particles, up to an additive constant proportional to $N$. The free energy thus determined contains the Gibbs factorial $N!$ in addition to the phase space integration of the Gibbs-Boltzmann factor. The key step in the derivation is to construct a quasi-static decomposition of small thermodynamic systems.
