Entropy of a non-uniform one-dimensional fluid

A one-dimensional particle system with arbitrary nearest-neighbour interaction and arbitrary external field is investigated. The system is considered as an inverse problem, that of determining the internal and external interactions needed to produce given singlet and nearest-neighbour pair densities. The profile equations, the entropy functional which generates them, and the redefined direct correlation function are found exactly. Equivalent expressions are derived in which the full pair distribution and potential-range truncation are the controlling functions.