Sergio Simonella of the Department of Mathematics of Sapienza University of Rome was awarded a 1.4 million-euro ERC Consolidator grant for the KiLiM project on the physical-mathematical investigation of the kinetic theory of matter. The prestigious award, obtained in the 2023 call, will fund the study that aims to prove the validity of this theory, starting with an understanding of the underlying mathematical problems. These include equations that describe non-equilibrium processes such as transport mechanisms in fluids and gases. They have been in use for over 150 years, since the theories of J.C. Maxwell and L. Boltzmann, and constitute one of the most enduring and successful contributions in the history of science. Nevertheless, the properties of the kinetic equations pose mathematical problems of exceptional difficulty that have remained unsolved for decades. A rarefied gas, such as the air in the upper atmosphere, is made up of a multitude of particles invisible to the human eye, which collide with each other in an incessant, apparently random motion, but strictly governed by the fundamental laws of mechanics. The mathematical model for such dynamics is so complex as to be inaccessible to human technical capabilities. However, a probabilistic mathematical approach makes it possible to reduce the complexity and explain the global qualities of the system, such as diffusive phenomena and entropy growth.

The KiLiM project thus aims to study the impressive diversity of nature, from the microscopically small to the macroscopically large, with the objective of justifying, in a rigorous manner, the origin of the arrow of time and the transition from order to disorder.

To sum up, the team coordinated by Simonella will seek to prove the validity of kinetic theory, starting from the first principles that govern microscopic mechanics. Today, kinetic theory continues to find new applications in practical calculations and plays a central role in many areas of physics, astrophysics, chemistry, engineering and information theory.