  This paper gives a systematic method for constructing an N-body potential,
approximating the true potential, that accurately captures meso-scale behavior
of the chemical or biological system using pairwise potentials coming from
experimental data or ab initio methods. The meso-scale behavior is translated
into logic rules for the dynamics. Each pairwise potential has an associated
logic function that is constructed using the logic rules, a class of elementary
logic functions, and AND, OR, and NOT gates. The effect of each logic function
is to turn its associated potential on and off. The N-body potential is
constructed as linear combination of the pairwise potentials, where the
"coefficients" of the potentials are smoothed versions of the associated logic
functions. These potentials allow a potentially low-dimensional description of
complex processes while still accurately capturing the relevant physics at the
meso-scale. We present the proposed formalism to construct coarse-grained
potential models for three examples: an inhibitor molecular system, bond
breaking in chemical reactions, and DNA transcription from biology. The method
can potentially be used in reverse for design of molecular processes by
specifying properties of molecules that can carry them out.
