  Potential energy landscape (PEL) is essential to determine phase stability,
reaction path, and other important physical as well as chemical properties.
Whereas given PEL can reasonably determine the properties in thermodynamically
equilibrium state, it is generally unclear whether a set of known property can
uniquely and/or stably determines PEL, i.e., understandings of property/PEL
correspondence is basically unidirectional in the current statistical
mechanics. Here we make significant advance toward bidirectional bridging of
this gap for classical discrete systems under many-body interactions. Our idea
is to focus on characteristic microscopic geometry in configuration space for
an exactly solvable system, resulting in a new, important quantity of
"harmonicity in the structural degree of freedom". This quantity reasonablly
characterizes which structures in equilibrium state have practically unique and
stable correspondence to PEL, without requiring any thermodynamic information
such as energy or temperature. The present findings will open a gate to
constructing reliable PEL, where its predictive uncertainty can be a priori
known. A significant role of microscopic geometry for non-interacting system
should be re-emphasized in statistical mechanics.
