  Theoretical frameworks used to qualitatively and quantitatively describe
nuclear dynamics in solids are often based on the harmonic approximation.
However, this approximation is known to become inaccurate or to break down
completely in many modern functional materials. Interestingly, there is no
reliable measure to quantify anharmonicity so far. Thus, a systematic
classification of materials in terms of anharmonicity and a benchmark of
methodologies that may be appropriate for different strengths of anharmonicity
is currently impossible. In this work, we derive and discuss a statistical
measure that reliably classifies compounds across temperature regimes and
material classes by their "degree of anharmonicity". This enables us to
distinguish "harmonic" materials, for which anharmonic effects constitute a
small perturbation on top of the harmonic approximation, from strongly
"anharmonic" materials, for which anharmonic effects become significant or even
dominant and the treatment of anharmonicity in terms of perturbation theory is
more than questionable. We show that the analysis of this measure in real and
reciprocal space is able to shed light on the underlying microscopic
mechanisms, even at conditions close to, e.g., phase transitions or defect
formation. Eventually, we demonstrate that the developed approach is
computationally efficient and enables rapid high-throughput searches by
scanning over a set of several hundred binary solids. The results show that
strong anharmonic effects beyond the perturbative limit are not only active in
complex materials or close to phase transitions, but already at moderate
temperatures in simple binary compounds.
