{'fraction_non_alphanumeric': 0.015775635407537247, 'fraction_numerical': 0.0, 'mean_word_length': 5.488636363636363, '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}}
Homogeneous properties of modified renormalized density functional theory for non-uniform classical fluids

The author proposes the modified renormalized density functional theory (MRDFT) based on a global average of the density, and investigate some properties of this theory. In this approximation, the weighting function and the weighted density are determined by minimizing the free-energy functional with respect to the 'coarse-grained' density as a free variable. They show that this approximation also leads to the usual hypernetted chain (HNC) equation of state for the homogeneous systems as do the weighted density approximation theories based on the global average of the density, even though their free-energy functional forms and the weighting functions are basically different. From the derivation in the present work and comparison with the weighted density approximation theories based on the global average of the density, they also obtain the required conditions for the weighted density approximation theories based on a global average of the density to satisfy the usual HNC equation of state for the homogeneous systems.