{'fraction_non_alphanumeric': 0.01907356948228883, 'fraction_numerical': 0.0, 'mean_word_length': 5.336206896551724, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Statistical properties of two interacting soft spheres in a hard spherical pore

The structure and thermodynamics of two soft spheres, whose interactions include the soft repulsion and attraction, confined in a hard spherical pore have been considered. The exact partition function, one-body density, and equation of state have been obtained using the Fourier transform method. The pore-size and potential dependence of the structural and thermodynamic properties have been investigated. The two penetrable square-well spheres shows a negative compressibility of the van der Waals type, which imitates the phase transition of many particle system. The van der Waals instability for two penetrable square-well spheres has been studied.