  For classical discrete systems under constant composition, it has been
considered that genuine thermodynamic variables such as free energy cannot be
generally determined from information about a single or a few selected
microscopic states. Despite this fact, we here show that Helmholtz free energy
for any given composition for disordered states can be well characterized by
information about a few (R+3, where R denotes number of components) specially
selected microscopic states, whose structure can be known a priori without
requiring any thermodynamic information. The present study is a non-trivial
extension of our recently-developed theoretical approach for special
microscopic states in canonical ensemble to semi-grand canonical ensemble,
which additionally enables to characterize temperature dependence of other
thermodynamic variables such as internal energy and entropy.
