Surface tension, hydrophobicity, and black holes: The entropic connection

The geometric entropy arising from partitioning space in a fluid ''field theory'' is shown to be linearly proportional to the area of an excluded region. The coefficient of proportionality is related to surface tension by a thermodynamic argument. Good agreement with experimental data is obtained for a number of fluids. The calculation employs a density-matrix formalism developed previously for studying the origin of black hole entropy. This approach may lead to a practical technique for the evaluation of thermodynamic quantities with important entropic components.