We develop a novel method to analyze the excluded volume of the multicomponent mixtures of classical hard spheres in the grand canonical ensemble. The method is based on the Laplace–Fourier transform technique and allows one to account for the fluctuations of the particle number density for the induced surface and curvature tensions equation of state. As a result one can go beyond the Van der Waals (VdW) approximation by obtaining the suppression of the induced surface and curvature tensions coefficients at moderate and high packing fractions. In contrast to the standard induced surface and curvature tensions equation of state the suppression of these coefficients is not the exponential, but a power-like one. The obtained alternative equation of state is further generalized to account for higher virial coefficients. This result is straightforwardly generalized to the case of quantum statistics.

我们开发了一种新方法来分析大正则系综中经典硬球的多组分混合物的排除体积。该方法基于拉普拉斯-傅立叶变换技术，可以解释诱导表面和曲率张力状态方程的粒子数密度波动。因此，通过在中等和高填充率下获得诱导表面和曲率张力系数的抑制，可以超越范德华 (VdW) 近似。与标准诱导表面和曲率张力状态方程相反，这些系数的抑制不是指数的，而是类似幂的。所获得的替代状态方程被进一步推广以解释更高的维里系数。