  For classical discrete system under constant composition, we theoretically
examine origin of nonlinearity in thermodynamic (so-called canonical) average
w.r.t. many-body interactions, in terms of geometrical information in
configuratin space. We clarify that nonlinearity essentially comes from
deviation in configurational density of states (CDOS) before applying many-body
interactions to the system, from multidimensional gaussian distribution. The
present finding strongly suggest the significance to investigate how the
deviation in CDOS bridges bidirectional stability relationships between
equilibrium structure and potential energy in thermodynamic average.
