The methodology developed by Lustig for calculating thermodynamic properties in the microcanonical and canonical ensembles [J. Chem. Phys. 100, 3048 (1994); Mol. Phys. 110, 3041 (2012)] is applied to derive rigorous expressions for thermodynamic properties of fluids in the grand canonical ensemble. All properties are expressed by phase-space functions, which are related to derivatives of the grand canonical potential with respect to the three independent variables of the ensemble: temperature, volume, and chemical potential. The phase-space functions contain ensemble averages of combinations of the number of particles, potential energy, and derivatives of the potential energy with respect to volume. In addition, expressions for the phase-space functions for temperature-dependent potentials are provided, which are required to account for quantum corrections semiclassically in classical simulations. Using the Lennard-Jones model fluid as a test case, the derived expressions are validated by Monte Carlo simulations. In contrast to expressions for the thermal expansion coefficient, the isothermal compressibility, and the thermal pressure coefficient from the literature, our expressions yield more reliable results for these properties, which agree well with a recent accurate equation of state for the Lennard-Jones model fluid. Moreover, they become equivalent to the corresponding expressions in the canonical ensemble in the thermodynamic limit.

中文翻译：

---

大正则系综中的经典统计力学

Lustig 开发的用于计算微正则和正则集合中热力学性质的方法 [ J. Chem. 物理。 100 , 3048 (1994); 摩尔。物理。 110, 3041 (2012)] 用于推导出正则系综中流体的热力学性质的严格表达式。所有属性都由相空间函数表示，这些函数与关于集合的三个独立变量的正则势的导数有关：温度、体积和化学势。相空间函数包含粒子数、势能和势能相对于体积的导数的组合的系综平均值。此外，还提供了温度相关势的相空间函数的表达式，这是在经典模拟中半经典地解释量子校正所必需的。使用 Lennard-Jones 模型流体作为测试案例，派生的表达式通过蒙特卡罗模拟进行验证。与文献中的热膨胀系数、等温压缩率和热压系数的表达式相比，我们的表达式为这些属性产生了更可靠的结果，这与最近 Lennard-Jones 模型流体的精确状态方程非常吻合. 此外，它们等效于热力学极限中正则系综中的相应表达式。