The locally enhanced sampling (LES) approximation used in molecular modeling is analytically derived for a simple quadratic energy function. Starting With multiple copies of full protein-ligand complexes the thermodynamic probability distribution is reduced to that of a complex with a single protein and multiple ligands. The reduction of the protein phase space and the Hamiltonian obtained from the reduction suggest a new LES formalism, whose definition and interpretation are closely related to, but different from the traditional ones. One characteristic of the new formalism is that it is free from the inherent temperature disparity of the traditional LES. The error involved in the LES approximation is identified as the truncation of an induced inter-ligand interaction in the reduced Hamiltonian. This truncated term contains important information on the correlation between the protein intra-molecular and the protein-ligand inter-molecular interactions. These results may provide insight and guidance for interpreting and improving the LES simulations.