  A quantum system at equilibrium is represented by a corresponding classical
system, chosen to reproduce thermodynamic and structural properties. The
motivation is to allow application of classical strong coupling theories and
molecular dynamics simulation to quantum systems at strong coupling. The
correspondence is made at the level of the grand canonical ensembles for the
two systems. An effective temperature, local chemical potential, and pair
potential are introduced to define the corresponding classical system. These
are determined formally by requiring the equivalence of the grand potentials
and their functional derivatives. Practical inversions of these formal
definitions are indicated via the integral equations for densities and pair
correlation functions of classical liquid theory. Application to the ideal
Fermi gas is demonstrated, and the weak coupling form for the pair potential is
given. In a companion paper two applications are described: the thermodynamics
and structure of uniform jellium over a range of temperatures and densities,
and the shell structure of harmonically bound charges.
