News + Trends
Volcanic eruptions paved the way for the plague
by Spektrum der Wissenschaft
Why shards obey a hidden rule
17.12.2025
Translation: machine translated
Fragments do not form as randomly as expected. New calculations show: No matter what breaks, the size of the debris follows a universal mathematical law.
Marble, stone and iron break - and each shattered material ends in individual chaos, seemingly unpredictable. Or does it? Despite all the chemical and material differences, fragments apparently obey an astonishingly simple rule, as physicist Emmanuel Villermaux from the University of Aix-Marseille and the Institut Universitaire de France in Paris has discovered.
Villermaux found out: No matter what type of object shatters and how many pieces it shatters into - the size of the fragments is determined by a power law. The researcher derived this by analysing a fundamental thermodynamic property known as entropy. Put simply, this is a measure of the disorder of a system. More precisely, entropy is related to the number of possible states.
In his search for a universal law, Villermaux first looked at the result. He asked: In which state is a shattered object most likely to be found? Entropy was supposed to provide the answer. Because almost anything can shatter in countless equivalent ways, the end result should be the one that maximises entropy. From a mathematical point of view, this leads to an exponential distribution with many small and few large fragments.
The exact exponent in Villermaux's power law depends on the dimensions of the shattered object. For almost one-dimensional objects such as spaghetti or glass rods, the value is around 1.3; for almost two-dimensional porcelain plates, it is around 2.4, while an exponent of 3.5 applies to three-dimensional sugar cubes.
The physicist verified this by smashing several such sugar cubes and measuring the size distribution of the lumps. The law also matched the literature values from other experiments. Even material-specific differences can be summarised in the formula, for example between brittle objects such as glass and softer ones such as plastic. Depending on this, only the exponent changes, not the fundamental behaviour. Similarly, the force only makes a quantitative difference: a plate that falls to the floor with more force merely shatters into more fragments. However, their size ratios are distributed in exactly the same way.
How an object shatters therefore depends not so much on its microscopic properties as on fundamental statistical laws. However, Villermaux only looked at the size distribution of the fragments. The study leaves open how their individual geometric shape comes about. Materials research therefore still has work to do on the way to an ultimate world formula for shattering.
Spectrum of Science
We are partners of Spektrum der Wissenschaft and want to make well-founded information more accessible to you. Follow Spektrum der Wissenschaft if you like the articles.
Original article on Spektrum.de
Header image: Shutterstock / Anna Klymchuk
Spektrum der Wissenschaft
Wissenschaft aus erster Hand
dirdjaja@spektrum.deExperts from science and research report on the latest findings in their fields – competent, authentic and comprehensible.
Home + Kitchen
Follow topics and stay updated on your areas of interest
News + Trends
From the latest iPhone to the return of 80s fashion. The editorial team will help you make sense of it all.
Show all
